Relevant bibliographies by topics / Ultrafilters

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  2. Dissertations / Theses
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Academic literature on the topic 'Ultrafilters'

Author: Grafiati
Published: 4 June 2021
Last updated: 25 April 2022

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Journal articles on the topic "Ultrafilters"

1

Benedikt, Michael. "Ultrafilters which extend measures." Journal of Symbolic Logic 63, no. 2 (June 1998): 638–62. http://dx.doi.org/10.2307/2586856.

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AbstractWe study classes of ultrafilters on ω defined by a natural property of the Loeb measure in the Nonstandard Universe corresponding to the ultrafilter. This class, the Property M ultrafilters, is shown to contain all ultrafilters built up by taking iterated products over collections of pairwise nonisomorphic selective ultrafilters. Results on Property M ultrafilters are applied to the construction of extensions of probability measures, and to the study of measurable reductions between ultrafilters.
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Baumgartner, James E. "Ultrafilters on ω." Journal of Symbolic Logic 60, no. 2 (June 1995): 624–39. http://dx.doi.org/10.2307/2275854.

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AbstractWe study the I-ultrafilters on ω, where I is a a collection of subsets of a set X, usually ℝ or ω1. The I-ultrafilters usually contain the P-points, often as a small proper subset. We study relations between I-ultrafilters for various I, and closure of I-ultrafilters under ultrafilter sums. We consider, but do not settle, the question whether I-ultrafilters always exist.
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BLASS, ANDREAS, NATASHA DOBRINEN, and DILIP RAGHAVAN. "THE NEXT BEST THING TO A P-POINT." Journal of Symbolic Logic 80, no. 3 (July 22, 2015): 866–900. http://dx.doi.org/10.1017/jsl.2015.31.

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AbstractWe study ultrafilters on ω2 produced by forcing with the quotient of ${\cal P}$(ω2) by the Fubini square of the Fréchet filter on ω. We show that such an ultrafilter is a weak P-point but not a P-point and that the only nonprincipal ultrafilters strictly below it in the Rudin–Keisler order are a single isomorphism class of selective ultrafilters. We further show that it enjoys the strongest square-bracket partition relations that are possible for a non-P-point. We show that it is not basically generated but that it shares with basically generated ultrafilters the property of not being at the top of the Tukey ordering. In fact, it is not Tukey-above [ω1]<ω, and it has only continuum many ultrafilters Tukey-below it. A tool in our proofs is the analysis of similar (but not the same) properties for ultrafilters obtained as the sum, over a selective ultrafilter, of nonisomorphic selective ultrafilters.
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Barney, Christopher. "Ultrafilters on the natural numbers." Journal of Symbolic Logic 68, no. 3 (September 2003): 764–84. http://dx.doi.org/10.2178/jsl/1058448437.

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AbstractWe study the problem of existence and generic existence of ultrafilters on ω. We prove a conjecture of Jörg Brendle's showing that there is an ultrafilter that is countably closed but is not an ordinal ultrafilter under CH. We also show that Canjar's previous partial characterization of the generic existence of Q-points is the best that can be done. More simply put, there is no normal cardinal invariant equality that fully characterizes the generic existence of Q-points. We then sharpen results on generic existence with the introduction of σ-compact ultrafilters. We show that the generic existence of said ultrafilters is equivalent to . This result, taken along with our result that there exists a Kσ, non-countably closed ultrafilter under CH, expands the size of the class of ultrafilters that were known to fit this description before. From the core of the proof, we get a new result on the cardinal invariants of the continuum, i.e., the cofinality of the sets with σ-compact closure is .
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Fremlin, D. H., and P. J. Nyikos. "Saturating ultrafilters on N." Journal of Symbolic Logic 54, no. 3 (September 1989): 708–18. http://dx.doi.org/10.2307/2274735.

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AbstractWe discuss saturating ultrafilters on N, relating them to other types of non-principal ultrafilter. (a) There is an (ω, c)-saturating ultrafllter on N iff 2λ ≤ c for every λ < c and there is no cover of R by fewer than c nowhere dense sets, (b) Assume Martin's axiom. Then, for any cardinal κ, a nonprincipal ultrafllter on N is (ω, κ)-saturating iff it is almost κ-good. In particular, (i) p(κ)-point ultrafilters are (ω, κ)-saturating, and (ii) the set of (ω, κ)-saturating ultrafilters is invariant under homeomorphisms of βN/N. (c) It is relatively consistent with ZFC to suppose that there is a Ramsey p(c)-point ultrafilter which is not (ω, c)-saturating.
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Kanamori, Akihiro. "Finest partitions for ultrafilters." Journal of Symbolic Logic 51, no. 2 (June 1986): 327–32. http://dx.doi.org/10.1017/s0022481200031182.

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If a uniform ultrafilter U over an uncountable cardinal κ is not outright countably complete, probably the next best thing is that it have a finest partition: a master function f:κ → ω with ƒ−({n}) ∉ U for each n ϵ ω such that for any g: κ → κ, either (a) it is one-to-one on a set in U, or (b) it factors through ƒ (mod U), i.e. for some function h, {α < κ ∣ h(f(α)) = g(α)} ϵ U. In this paper, it is shown that recent contructions of irregular ultrafilters over ω1 can be amplified to incorporate a finest partition.Henceforth, let us assume that all ultrafilters are uniform.There has been an extensive study of substantial hypotheses, which are nonetheless weaker than countable completeness, on ultrafilters over uncountable cardinals. To survey some results and to establish a context, let us first recall the Rudin-Keisler (RK) ordering on ultrafilters: If Ui is an ultrafilter over Iii for i = 1, 2, then U1 ≤RKU2 iff there is a projecting function Ψ:I2 → I1 such that U1 = Ψ*(U2) = {X ⊆, I1∣ Ψ−1(X) ϵ U2}· U1, =RKU2 iff U1, ≤RK and U2 and U2≤RKU1; and U1<RKU2 iff U1≤RKU2 yet U1 ≠RKU2. In terms of this ordering, if an ultrafilter U has a finest partition ƒ, then ƒ*(U) over ω is maximum amongst all RK predecessors of U: for any g:κ → κ, if g*(U) <RKU, then g is not one-to-one on a set in U, so since g factors through ƒ with some h,g*(U) = h*(ƒ*(U)). Say now that an ultrafilter U over κ > ω is indecomposable iff whenever ω < λ < κ, there is no V ≤RKU such that V is a (uniform) ultrafilter over λ.
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Palumbo, Justin. "Comparisons of Polychromatic and Monochromatic Ramsey Theory." Journal of Symbolic Logic 78, no. 3 (September 2013): 951–68. http://dx.doi.org/10.2178/jsl.7803130.

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AbstractWe compare the strength of polychromatic and monochromatic Ramsey theory in several set-theoretic domains. We show that the rainbow Ramsey theorem does not follow from ZF, nor does the rainbow Ramsey theorem imply Ramsey's theorem over ZF. Extending the classical result of Erdős and Rado we show that the axiom of choice precludes the natural infinite exponent partition relations for polychromatic Ramsey theory. We introduce rainbow Ramsey ultrafilters, a polychromatic analogue of the usual Ramsey ultrafilters. We investigate the relationship of rainbow Ramsey ultrafilters with various special classes of ultrafilters, showing for example that every rainbow Ramsey ultrafilter is nowhere dense but rainbow Ramsey ultrafilters need not be rapid. This entails comparison of the polychromatic and monochromatic Ramsey theorems as combinatorial principles on ω.
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FERNÁNDEZ-BRETÓN, DAVID JOSÉ. "STABLE ORDERED UNION ULTRAFILTERS AND cov." Journal of Symbolic Logic 84, no. 3 (April 3, 2019): 1176–93. http://dx.doi.org/10.1017/jsl.2019.20.

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AbstractA union ultrafilter is an ultrafilter over the finite subsets of ω that has a base of sets of the form ${\text{FU}}\left( X \right)$, where X is an infinite pairwise disjoint family and ${\text{FU}}(X) = \left\{ {\bigcup {F|F} \in [X]^{ < \omega } \setminus \{ \emptyset \} } \right\}$. The existence of these ultrafilters is not provable from the $ZFC$ axioms, but is known to follow from the assumption that ${\text{cov}}\left( \mathcal{M} \right) = \mathfrak{c}$. In this article we obtain various models of $ZFC$ that satisfy the existence of union ultrafilters while at the same time ${\text{cov}}\left( \mathcal{M} \right) = \mathfrak{c}$.
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Baldwin, Stewart. "The ⊲-ordering on normal ultrafilters." Journal of Symbolic Logic 50, no. 4 (December 1985): 936–52. http://dx.doi.org/10.2307/2273982.

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If κ is a measurable cardinal, then it is a well-known fact that there is at least one normal ultrafilter over κ. In [K-1], Kunen showed that one cannot say more without further assumptions, for if U is a normal ultrafilter over κ, then L[U] is an inner model of ZFC in which κ has exactly one normal measure. On the other hand, Kunen and Paris showed [K-P] that if κ is measurable in the ground model, then there is a forcing extension in which κ has normal ultrafilters, so it is consistent that κ has the maximum possible number of normal ultrafilters. Starting with assumptions stronger than measurability, Mitchell [Mi-1] filled in the gap by constructing models of ZFC + GCH satisfying “there are exactly λ normal ultrafilters over κ”, where λ could be κ+ or κ++ (measured in the model), or anything ≤ κ. Whether or not Mitchell's results can be obtained by starting only with a measurable cardinal in the ground model and defining a forcing extension is unknown.There are substantial differences between the Mitchell models and the Kunen-Paris models. In the Kunen-Paris models κ can be the only measurable cardinal. However, in the Mitchell model in which κ has exactly 2 normal ultrafilters, one of them contains the set {α < κ: α is measurable} while the other does not. Thus it is natural to ask if it is possible to get a model M of ZFC in which κ is the only measurable cardinal and κ has exactly 2 normal ultrafilters. In this paper we will show that, using appropriate large cardinal assumptions, the answer is yes.
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Barbanel, Julius B. "On the relationship between the partition property and the weak partition property for normal ultrafilters on Pκλ." Journal of Symbolic Logic 58, no. 1 (March 1993): 119–27. http://dx.doi.org/10.2307/2275328.

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AbstractSuppose κ is a supercompact cardinal and λ > κ. We study the relationship between the partition properly and the weak partition properly for normal ultrafilters on Pκλ. On the one hand, we show that the following statement is consistent, given an appropriate large cardinal assumption: The partition property and the weak partition properly are equivalent, there are many normal ultrafilters that satisfy these properties, and there are many normal ultrafilters that do not satisfy these properties. On the other hand, we consider the assumption that, for some λ > κ, there exists a normal ultrafilter U on Pκλ such that U satisfies the weak partition property but does not satisfy the partition property. We show that this assumption is implied by the assertion that there exists a cardinal γ > κ such that γ is γ+-supercompact, and, assuming the GCH, it implies the assertion that there exists a cardinal γ > κ such that γ is a measurable cardinal with a normal ultrafilter concentrating on measurable cardinals.
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Dissertations / Theses on the topic "Ultrafilters"

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Nxumalo, Mbekezeli Sibahle. "Ultrafilters and Compactification." UWC, 2020. http://hdl.handle.net/11394/7374.

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>Magister Scientiae - MSc
In this thesis, we construct the ultrafilter space of a topological space using ultrafilters as points, study some of its properties and describe a method of generating compactifications through the ultrafilter space. As part of investigating some properties of the ultrafilter space, we show that the ultrafilter space forms a monad in the category of topological spaces. Furthermore, we show that rendering the ultrafilter space suitably separated results in a generation of separated compactifications which coincide with some well-known compactifications. When the ultrafilter space is rendered T0 or sober, the resulting compactifications is a stable Compactifications. Rendering the ultrafilter space T2 or Tychono results in the Stone_ Cechcompactification
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Devlin, Barry-Patrick. "Codensity, compactness and ultrafilters." Thesis, University of Edinburgh, 2016. http://hdl.handle.net/1842/19476.

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Codensity monads are ubiquitous, as are various different notions of compactness and finiteness. Two such examples of "compact" spaces are compact Hausdorff Spaces and Linearly Compact Vector Spaces. Compact Hausdorff Spaces are the algebras of the codensity monad induced by the inclusion of finite sets in the category of sets. Similarly linearly compact vector spaces are the algebras of the codensity monad induced by the inclusion of finite dimensional vector spaces in the category of vector spaces. So in these two examples the notions of finiteness, compactness and codensity are intertwined. In this thesis we generalise these results. To do this we generalise the notion of ultrafilter, and follow the intuition of the compact Hausdorff case. We give definitions of general notions of "finiteness" and "compactness" and show that the algebras for the codensity monad induced by the "finite" objects are exactly the "compact" objects.
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Krautzberger, Peter [Verfasser]. "Idempotent filters and ultrafilters / Peter Krautzberger." Berlin : Freie Universität Berlin, 2009. http://d-nb.info/1023817063/34.

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Boero, Ana Carolina. "Topologias enumeravelmente compactas em grupos abelianos de não torção via ultrafiltros seletivos." Universidade de São Paulo, 2011. http://www.teses.usp.br/teses/disponiveis/45/45131/tde-23082011-225107/.

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Assumindo a existência de $\\mathfrak c$ ultrafiltros seletivos dois a dois incomparáveis (segundo a ordem de Rudin-Keisler) provamos que o grupo abeliano livre de cardinalidade $\\mathfrak c$ admite uma topologia de grupo enumeravelmente compacta com uma seqüência não trivial convergente. Sob as mesmas hipóteses, mostramos que um grupo topológico abeliano quase livre de torção $(G, +, \\tau)$ com $|G| = |\\tau| = \\mathfrak c$ admite uma topologia independente de $\\tau$ que o torna um grupo topológico e caracterizamos algebricamente os grupos abelianos de não torção que têm cardinalidade $\\mathfrak c$ e que admitem uma topologia de grupo enumeravelmente compacta (sem seqüências não triviais convergentes). Provamos, ainda, que o grupo abeliano livre de cardinalidade $\\mathfrak c$ admite uma topologia de grupo que torna seu quadrado enumeravelmente compacto e construímos um semigrupo de Wallace cujo quadrado é, também, enumeravelmente compacto. Por fim, assumindo a existência de $2^{\\mathfrak c}$ ultrafiltros seletivos, garantimos que se um grupo abeliano de não torção e cardinalidade $\\mathfrak c$ admite uma topologia de grupo enumeravelmente compacta, então o mesmo admite $2^{\\mathfrak c}$ topologias de grupo enumeravelmente compactas (duas a duas não homeomorfas).
Assuming the existence of $\\mathfrak c$ pairwise incomparable selective ultrafilters (according to the Rudin-Keisler ordering) we prove that the free abelian group of cardinality $\\mathfrak c$ admits a countably compact group topology that contains a non-trivial convergent sequence. Under the same hypothesis, we show that an abelian almost torsion-free topological group $(G, +, \\tau)$ with $|G| = |\\tau| = \\mathfrak c$ admits a group topology independent of $\\tau$ and we algebraically characterize the non-torsion abelian groups of cardinality $\\mathfrak c$ which admit a countably compact group topology (without non-trivial convergent sequences). We also prove that the free abelian group of cardinality $\\mathfrak c$ admits a group topology that makes its square countably compact and we construct a Wallace\'s semigroup whose square is countably compact. Finally, assuming the existence of $2^$ selective ultrafilters, we ensure that if a non-torsion abelian group of cardinality $\\mathfrak c$ admits a countably compact group topology, then it admits $2^$ (pairwise non-homeomorphic) countably compact group topologies.
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Bishop, Gregory J. "Ultrafilters generated by a closed set of functions and K- covering sets /." The Ohio State University, 1992. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487779914823645.

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Koçak, Mahmut. "Compactifications of a uniform space and the LUC-compactification of the real numbers in terms of the concept of near ultrafilters." Thesis, University of Hull, 1994. http://hydra.hull.ac.uk/resources/hull:10782.

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Machado, Geovani Pereira. "Introdução à análise não standard." Universidade de São Paulo, 2018. http://www.teses.usp.br/teses/disponiveis/45/45131/tde-18022019-171451/.

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A área conhecida como Análise Não Standard consiste na aplicação dos métodos da Teoria dos Modelos e da Teoria dos Ultrafiltros para a obtenção de extensões peculiares de sistemas matemáticos infinitos. As novas estruturas construídas segundo esse procedimento satisfazem ao Princípio da Transferência, uma propriedade de suma importância e influência a qual afirma que as mesmas sentenças de primeira ordem com quantificadores limitados são verdadeiras para o sistema original e a sua extensão. Concebida em 1961 por Abraham Robinson e aprimorada por vários matemáticos nos anos subsequentes, tal área de pesquisa provou ser bastante proveitosa e esclarecedora para diversas outras partes da Matemática, como a Topologia, a Teoria das Probabilidades, a Análise Funcional e a Análise Complexa. Manifesta-se uma reavaliação da Teoria dos Domínios Ordenados seguida de um tratamento completo e gradual das fundações da Análise Não Standard assumindo a perspectiva dos Monomorfismos Não Standard, onde adota-se como metateoria a teoria dos conjuntos de Neumann-Bernays-Gödel com o Axioma da Escolha. A fim de impulsionar a assimilação da metodologia abordada, o estudo explora as propriedades do corpo não arquimediano dos números hiper-reais de maneira intuitiva e informal, utilizando-se destas para revelar demonstrações alternativas e relativamente diretas de alguns dos principais resultados do Cálculo Diferencial e Integral, como o Teorema do Valor Intermediário, o Teorema de Bolzano-Weierstrass, o Teorema do Ponto Crítico, o Teorema da Função Inversa e o Teorema Fundamental do Cálculo.
The field known as Non-standard Analysis consists in the application of the methods of Model Theory and Ultrafilter Theory to the attainment of peculiar extensions of infinite mathematical systems. The new structures produced under that procedure satisfy the Transfer Principle, a property of the utmost importance and influence which states that the same first-order sentences with bounded quantifiers are true for the original system and its extension. Conceived in 1961 by Abraham Robinson and improved by a number of mathematicians in the following years, such area of research has proved to be very fruitful and illuminating to many other parts of Mathematics, such as Topology, Probability Theory, Functional Analysis and Complex Analysis. The work presents a reexamination of the Theory of Ordered Domains followed by a thorough and gradual treatment of the foundations of Non-standard Analysis under the perspective of Non-standard Monomorphisms, where Neumann-Bernays-Gödels set theory with the Axiom of Choice is adopted as metatheory. In order to boost the assimilation of the methodology put forward, the study explores the properties of the non-archimedean field of hyperreal numbers in an intuitive and informal fashion, employing them to reveal alternative and relatively direct proofs of some of the main results of Differential and Integral Calculus, such as the Intermediate Value Theorem, the Bolzano-Weierstrass Theorem, the Extreme Value Theorem, the Inverse Function Theorem and the Fundamental Theorem of Calculus.
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Eliasson, Jonas. "Ultrasheaves." Doctoral thesis, Uppsala : Matematiska institutionen, Univ. [distributör], 2003. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-3762.

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Quiroga, Jury Fabiana Castiblanco. "Topologias de grupo enumeravelmente compactas: MA, forcing e ultrafiltros seletivos." Universidade de São Paulo, 2011. http://www.teses.usp.br/teses/disponiveis/45/45131/tde-07092012-163026/.

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É bem conhecido o fato de que todo grupo compacto tem sequências não triviais convergentes. A existência de grupos enumeravelmente compactos sem sequências não triviais convergentes, foi provada usando axiomas adicionais à axiomática usual ZFC: A. Hajnal e I. Juhász sob CH, E. K. van Douwen sob MA, A. H. Tomita sob MA(sigma-centrada) e R.E. Madariaga-Garcia e A. H. Tomita usando ultrafiltros seletivos. Neste trabalho, estudaremos algumas construções recentes relacionadas com as citadas acima, usando o Axioma de Martin, ultrafiltros seletivos e forcing. Essas construções estão relacionadas com algumas questões indicadas por A.D. Wallace, E. van Douwen, M. Tkachenko, D. Dikranjan e D. Shakhmatov
It is well known that every compact group has non-trivial convergent sequences. The existence of countably compact groups without non-trivial convergent sequences was proved using extra set-theoretical assumptions: A. Hajnal and I. Juhasz under CH, E. K. van Douwen under MA, A.H.Tomita under MA(centered) and R.E.Madariaga-Garcia and A.H. Tomita using a selective ultrafilter. I n this work, we study some recent constructions related to the ones given above using Martin Axiom, selective ultrafilters and forcing, related to questions raised by A.D. Wallace, E. van Douwen, M. Tkacenko, D. Dikranjan and D. Shakhmatov.
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Ruotsalainen, V. (Vesa). "Nephrin:role in the renal ultrafilter and involvement in proteinuria." Doctoral thesis, University of Oulu, 2004. http://urn.fi/urn:isbn:9514273494.

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Abstract Congenital nephrotic syndrome of the Finnish type (NPHS1, CNF) is an autosomal recessive disease that affects 1:8000 newborns in Finland. NPHS1 is characterised by heavy proteinuria already in utero and typical signs of nephrotic syndrome (NS) are present at or soon after birth. Due to the evident absence of extrarenal symptoms, NPHS1 has been considered a model disease for NS. In this study, the NPHS1 locus on chromosome 19q13.1 was sequenced and analysed with computer programs to identify new genes in the region. Genes were further characterised and sequenced from NPHS1 patient samples, as well as from controls. Analysis of the data resulted in the identification of the affected gene with two mutations that were found to explain 94% of the Finnish NPHS1 cases. The NPHS1 gene was found to encode a novel single-pass transmembrane protein, termed nephrin, which belongs to the immunoglobulin superfamily of cell adhesion molecules. The NPHS1 gene was cloned and recombinant nephrin fragments were produced in prokaryotic and eukaryotic expression systems. These fragments were used to raise antibodies that were utilized to characterise the spatial and temporal expression of nephrin in kidney glomeruli. Nephrin was localised by electron microscopy (EM) in ladder-like structures of the early junctional complexes of developing columnar podocytes at the capillary stage. In mature glomeruli, nephrin was localised to the slit diaphragm (SD) between adjacent glomerular podocyte foot processes. In order to investigate the more general involvement of nephrin in proteinuric disease, its expression was studied in primary acquired NS by immunofluorescence microscopy. The level of nephrin expression was found to be significantly reduced in membranous glomerulonephritis, minimal change disease and in focal segmental glomerulosclerosis. The known effects of nephrin mutations, together with the structure predicted from its sequence and localisation of the protein to the SD, emphasizes its indispensable role in maintaining the integrity of the glomerular filtration barrier. The glomerular basement membrane has long been considered to possess the size-selective filtration property of the filtration barrier. However, the identification of nephrin in the SD, as well as its alterations in proteinuria, has led us to reconsider SD as the final decisive size-selective filter.
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Books on the topic "Ultrafilters"

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Bergelson, Vitaly, Andreas Blass, Mauro Di Nasso, and Renling Jin, eds. Ultrafilters across Mathematics. Providence, Rhode Island: American Mathematical Society, 2010. http://dx.doi.org/10.1090/conm/530.

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Ultrafilters and topologies on groups. Berlin: De Gruyter, 2011.

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1950-, Bergelson V. (Vitaly), ed. Ultrafilters across mathematics: International congress, Ultramath 2008, Applications of Ultrafilters and Ultraproducts in Mathematics, June 1-7, 2008, Pisa, Italy. Providence, R.I: American Mathematical Society, 2010.

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Filters and ultrafilters over definable subsets of admissible ordinals. Amsterdam, The Netherlands: Centrum voor Wiskunde en Informatica, 1986.

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Protasov, I. Combinatorics of numbers. Lviv, Ukraine: VNTL Publishers, 1997.

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Protasov, I. Combinatorics of numbers. Lviv: VNTL Publishers, 1997.

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Berg, Jan. Ontology without ultrafilters and possible worlds: An examination of Bolzano's ontology. Sankt Augustin: Academia, 1992.

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The Theory of Ultrafilters. Springer, 2012.

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Zelenyuk, Yevhen. Ultrafilters and Topologies on Groups. De Gruyter, Inc., 2011.

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Betancur, Carmen L. Some microbiological and sensory characteristics of Cheddar cheese manufactured from conventional and ultrafiltered-concentrated milk. 1988.

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Book chapters on the topic "Ultrafilters"

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Ceccherini-Silberstein, Tullio, and Michel Coornaert. "Ultrafilters." In Springer Monographs in Mathematics, 409–16. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-14034-1_18.

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Nasso, Mauro Di, Isaac Goldbring, and Martino Lupini. "Ultrafilters." In Nonstandard Methods in Ramsey Theory and Combinatorial Number Theory, 3–10. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-17956-4_1.

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Monk, J. Donald. "Number of Ultrafilters." In Cardinal Invariants on Boolean Algebras, 489. Basel: Springer Basel, 2014. http://dx.doi.org/10.1007/978-3-0348-0730-2_20.

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Brown, Nathanial, and Narutaka Ozawa. "Ultrafilters and ultraproducts." In Graduate Studies in Mathematics, 445–48. Providence, Rhode Island: American Mathematical Society, 2008. http://dx.doi.org/10.1090/gsm/088/18.

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García-Ferreira, S., and Y. F. Ortiz-Castillo. "Pseudocompactness and Ultrafilters." In Pseudocompact Topological Spaces, 77–105. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-91680-4_3.

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Monk, J. Donald. "Number of ultrafilters." In Cardinal Invariants on Boolean Algebras, 232. Basel: Birkhäuser Basel, 1996. http://dx.doi.org/10.1007/978-3-0346-0334-8_20.

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Monk, J. Donald. "Number of Ultrafilters." In Cardinal Functions on Boolean Algebras, 117. Basel: Birkhäuser Basel, 1990. http://dx.doi.org/10.1007/978-3-0348-6381-0_18.

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Blass, Andreas. "Kleene degrees of ultrafilters." In Lecture Notes in Mathematics, 29–48. Berlin, Heidelberg: Springer Berlin Heidelberg, 1985. http://dx.doi.org/10.1007/bfb0076213.

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Di Nasso, Mauro. "Hypernatural Numbers as Ultrafilters." In Nonstandard Analysis for the Working Mathematician, 443–74. Dordrecht: Springer Netherlands, 2015. http://dx.doi.org/10.1007/978-94-017-7327-0_11.

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Odifreddi, Piergiorgio. "Ultrafilters, Dictators, and Gods." In Finite Versus Infinite, 239–45. London: Springer London, 2000. http://dx.doi.org/10.1007/978-1-4471-0751-4_16.

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Conference papers on the topic "Ultrafilters"

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FLAŠKOVÁ, J. "${\cal I}$-ultrafilters and summable ideals." In 10th Asian Logic Conference. WORLD SCIENTIFIC, 2009. http://dx.doi.org/10.1142/9789814293020_0005.

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Hao, Song, Zheng Mingfa, and Song Xiuchao. "The Classification of the Filters and the Construction of the Free Ultrafilters." In 2015 Seventh International Conference on Measuring Technology and Mechatronics Automation (ICMTMA). IEEE, 2015. http://dx.doi.org/10.1109/icmtma.2015.279.

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Benzmüller, Christoph. "A (Simplified) Supreme Being Necessarily Exists, says the Computer: Computationally Explored Variants of Gödel's Ontological Argument." In 17th International Conference on Principles of Knowledge Representation and Reasoning {KR-2020}. California: International Joint Conferences on Artificial Intelligence Organization, 2020. http://dx.doi.org/10.24963/kr.2020/80.

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Abstract:
An approach to universal (meta-)logical reasoning in classical higher-order logic is employed to explore and study simplifications of Kurt Gödel's modal ontological argument. Some argument premises are modified, others are dropped, modal collapse is avoided and validity is shown already in weak modal logics K and T. Key to the gained simplifications of Gödel's original theory is the exploitation of a link to the notions of filter and ultrafilter in topology. The paper illustrates how modern knowledge representation and reasoning technology for quantified non-classical logics can contribute new knowledge to other disciplines. The contributed material is also well suited to support teaching of non-trivial logic formalisms in classroom.
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Reports on the topic "Ultrafilters"

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Stewart, C. A. The effects of tributyl phosphate on a polymeric ultrafilter. Office of Scientific and Technical Information (OSTI), August 1990. http://dx.doi.org/10.2172/6288047.

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