Relevant bibliographies by topics / Axiomas de Hilbert

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Academic literature on the topic 'Axiomas de Hilbert'

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Published: 4 June 2021
Last updated: 1 February 2022

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Journal articles on the topic "Axiomas de Hilbert"

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Zeman, Jan. "Hilbertova aritmetizace geometrie." FILOSOFIE DNES 10, no. 1 (April 13, 2019): 45–63. http://dx.doi.org/10.26806/fd.v10i1.269.

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Tato práce se podrobně věnuje způsobu, jakým David Hilbert (1862–1943) pojal aritmetizaci geometrie v knize Grundlagen der Geometrie z roku 1899. Nejprve stručně představíme Hilbertovy předchůdce z téže doby, kteří buď po změnách v založení geometrie volali, nebo je již sami prostřednictvím axiomaticko-deduktivní metody zapracovali. Neopomeneme přitom, co dílu předcházelo v dřívějších Hilbertových přednáškách. Následně se pokusíme nastínit­ obsah prvních dvou kapitol knihy a vysvětlit dobové i věcné souvislosti, nutné k jejich pochopení. Představíme způsob implicitních definic základních pojmů a vztahů v axiomech, a dále Hilbertovo rozdělení axiomů do skupin, přičemž se zejména zaměříme na axiomy spojitosti v kontextu s otázkou o její bezespornosti. K tomu popíšeme konstrukci aritmetického modelu axiomů geometrie, který Hilbert pro důkaz bezespornosti používá. V závěru se pokusíme nastínit hlavní důvody, které Hilberta k napsání díla vedly, a některé klíčové důsledky jeho pojetí axiomatiky geometrie.
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Arboleda Aparicio, Luis Carlos. "Introducción de la topología de vecindades en los trabajos de Fréchet y Hausdorff." Revista de la Academia Colombiana de Ciencias Exactas, Físicas y Naturales 41, no. 161 (January 12, 2018): 528. http://dx.doi.org/10.18257/raccefyn.510.

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En la primera parte, retomamos testimonios de Fréchet sobre la naturaleza de sus primeros trabajos (1904-1906) en los campos emergentes del Análisis funcional y Análisis general, en relación con su idea de introducir una estructura topológica en un espacio abstracto. En la segunda parte, destacamos la influencia que tuvo en esta idea, el punto de vista algebraico de la época de extender las nociones cantorianas a un espacio abstracto con una estructura de grupo finito. Fréchet supo aprovechar técnicas como el “modo de composición” entre los elementos del espacio, para axiomatizar operaciones y estructuras de la “clase L” con convergencia secuencial, la “clase V” con sistema de vecindades, la “clase E” con “écart” (métrica). Luego se aprovechan nuevos datos históricos para reafirmar la proximidad de las concepciones filosóficas subyacentes a estas investigaciones, con las ideas de Leibniz, específicamente en cuanto al método de “análisis de los principios”. En la tercera parte se estudia la contribución de Hausdorff de 1912 y 1914 al establecimiento de la axiomática de las vecindades para la topología de un espacio abstracto. Teniendo en cuenta las observaciones de Weyl y Bourbaki de que Hausdorff se inspiró para ello en Hilbert, se examina el sistema de axiomas para las vecindades del plano introducido por Hilbert en dos trabajos de 1902 consagrados al problema de la continuidad del espacio. Se exploran las conexiones del “espacio topológico” de Hausdorff basado en las vecindades, con las nociones de métrica, convergencia secuencial y vecindades propuestas años antes por Fréchet. Hausdorff insistió desde el comienzo que la topología del espacio separable tenía las características de generalidad y rigor formal que le permitían adaptarse a las aplicaciones mejor que otras. Se mostrará que todo ello era consistente con los ideales de simplicidad, unidad y economía de pensamiento que Hausdorff había adquirido en sus trabajos filosóficos tempranos. © 2017. Acad. Colomb. Cienc. Ex. Fis. Nat.
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Negri, Sara, and Jan von Plato. "From mathematical axioms to mathematical rules of proof: recent developments in proof analysis." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 377, no. 2140 (January 21, 2019): 20180037. http://dx.doi.org/10.1098/rsta.2018.0037.

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A short text in the hand of David Hilbert, discovered in Göttingen a century after it was written, shows that Hilbert had considered adding a 24th problem to his famous list of mathematical problems of the year 1900. The problem he had in mind was to find criteria for the simplicity of proofs and to develop a general theory of methods of proof in mathematics. In this paper, it is discussed to what extent proof theory has achieved the second of these aims. This article is part of the theme issue ‘The notion of ‘simple proof’ - Hilbert's 24th problem’.
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Raftery, J. G. "Correspondences between gentzen and hilbert systems." Journal of Symbolic Logic 71, no. 3 (September 2006): 903–57. http://dx.doi.org/10.2178/jsl/1154698583.

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Most Gentzen systems arising in logic contain few axiom schemata and many rule schemata. Hilbert systems, on the other hand, usually contain few proper inference rules and possibly many axioms. Because of this, the two notions tend to serve different purposes. It is common for a logic to be specified in the first instance by means of a Gentzen calculus, whereupon a Hilbert-style presentation ‘for’ the logic may be sought—or vice versa. Where this has occurred, the word ‘for’ has taken on several different meanings, partly because the Gentzen separator ⇒ can be interpreted intuitively in a number of ways. Here ⇒ will be denoted less evocatively by ⊲.In this paper we aim to discuss some of the useful ways in which Gentzen and Hilbert systems may correspond to each other. Actually, we shall be concerned with the deducibility relations of the formal systems, as it is these that are susceptible to transformation in useful ways. To avoid potential confusion, we shall speak of Hilbert and Gentzen relations. By a Hilbert relation we mean any substitution-invariant consequence relation on formulas—this comes to the same thing as the deducibility relation of a set of Hilbert-style axioms and rules. By a Gentzen relation we mean the fully fledged generalization of this notion in which sequents take the place of single formulas. In the literature, Hilbert relations are often referred to as sentential logics. Gentzen relations as defined here are their exact sequential counterparts.
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Coghetto, Roland, and Adam Grabowski. "Tarski Geometry Axioms – Part II." Formalized Mathematics 24, no. 2 (June 1, 2016): 157–66. http://dx.doi.org/10.1515/forma-2016-0012.

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Summary In our earlier article [12], the first part of axioms of geometry proposed by Alfred Tarski [14] was formally introduced by means of Mizar proof assistant [9]. We defined a structure TarskiPlane with the following predicates: of betweenness between (a ternary relation), of congruence of segments equiv (quarternary relation), which satisfy the following properties: congruence symmetry (A1), congruence equivalence relation (A2), congruence identity (A3), segment construction (A4), SAS (A5), betweenness identity (A6), Pasch (A7). Also a simple model, which satisfies these axioms, was previously constructed, and described in [6]. In this paper, we deal with four remaining axioms, namely: the lower dimension axiom (A8), the upper dimension axiom (A9), the Euclid axiom (A10), the continuity axiom (A11). They were introduced in the form of Mizar attributes. Additionally, the relation of congruence of triangles cong is introduced via congruence of sides (SSS). In order to show that the structure which satisfies all eleven Tarski’s axioms really exists, we provided a proof of the registration of a cluster that the Euclidean plane, or rather a natural [5] extension of ordinary metric structure Euclid 2 satisfies all these attributes. Although the tradition of the mechanization of Tarski’s geometry in Mizar is not as long as in Coq [11], first approaches to this topic were done in Mizar in 1990 [16] (even if this article started formal Hilbert axiomatization of geometry, and parallel development was rather unlikely at that time [8]). Connection with another proof assistant should be mentioned – we had some doubts about the proof of the Euclid’s axiom and inspection of the proof taken from Archive of Formal Proofs of Isabelle [10] clarified things a bit. Our development allows for the future faithful mechanization of [13] and opens the possibility of automatically generated Prover9 proofs which was useful in the case of lattice theory [7].
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Richter, William, Adam Grabowski, and Jesse Alama. "Tarski Geometry Axioms." Formalized Mathematics 22, no. 2 (June 30, 2014): 167–76. http://dx.doi.org/10.2478/forma-2014-0017.

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Summary This is the translation of the Mizar article containing readable Mizar proofs of some axiomatic geometry theorems formulated by the great Polish mathematician Alfred Tarski [8], and we hope to continue this work. The article is an extension and upgrading of the source code written by the first author with the help of miz3 tool; his primary goal was to use proof checkers to help teach rigorous axiomatic geometry in high school using Hilbert’s axioms. This is largely a Mizar port of Julien Narboux’s Coq pseudo-code [6]. We partially prove the theorem of [7] that Tarski’s (extremely weak!) plane geometry axioms imply Hilbert’s axioms. Specifically, we obtain Gupta’s amazing proof which implies Hilbert’s axiom I1 that two points determine a line. The primary Mizar coding was heavily influenced by [9] on axioms of incidence geometry. The original development was much improved using Mizar adjectives instead of predicates only, and to use this machinery in full extent, we have to construct some models of Tarski geometry. These are listed in the second section, together with appropriate registrations of clusters. Also models of Tarski’s geometry related to real planes were constructed.
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Torres Alcaraz, Carlos. "Hilbert, Kant y el fundamento de las matemáticas." Theoría. Revista del Colegio de Filosofía, no. 8-9 (December 31, 1999): 111–29. http://dx.doi.org/10.22201/ffyl.16656415p.1999.8-9.225.

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This paper looks into Hilbert’s thought about mathematics and explores its relation which the philosophy of Kant. The focus of the research is in the role of axiomatic thinking and logical analysis in foundational studies. The paper concentrates mainly in Hilbert’s research regarding the foundations of geometry, and follows his main lines of thought up to his programme, which revolves around a consistency proof for the axioms of classical mathematics. A final analysis allows us to conclude that for him mathematics is, in a broad sense, “the science of that which is possible” in this point, Hilbert diverges from Kant, even though he considers that classical mathematics has in its core a content, a view which separates him from the extreme formalism some times ascribed to him.
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Fontanella, Laura. "Axioms as Definitions: Revisiting Poincaré and Hilbert." Philosophia Scientae, no. 23-1 (February 18, 2019): 167–83. http://dx.doi.org/10.4000/philosophiascientiae.1827.

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Burn, R. P. "Non-Desarguesian planes and weak associativity." Mathematical Gazette 101, no. 552 (October 16, 2017): 458–64. http://dx.doi.org/10.1017/mag.2017.127.

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During the 19th century various criticisms of Euclid's geometry emerged and alternative axiom systems were constructed. That of David Hilbert ([1], 1899) paid particular attention to the independence of the axioms, and it is his insights which have shaped many of the further developments during the 20th century.We can, from his insights, define an affine plane as a set of points, with distinguished subsets called lines such thatAxiom 1: Given two distinct points, there is a unique line containing them both.Axiom 2: Given a line L and a point, p, not contained in L, there is a unique line containing p which does not intersect L.Axiom 3: There exist at least three points, not belonging to the same line.
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D'Ariano, Giacomo Mauro. "The solution of the sixth Hilbert problem: the ultimate Galilean revolution." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 376, no. 2118 (March 19, 2018): 20170224. http://dx.doi.org/10.1098/rsta.2017.0224.

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I argue for a full mathematization of the physical theory, including its axioms, which must contain no physical primitives. In provocative words: ‘physics from no physics’. Although this may seem an oxymoron, it is the royal road to keep complete logical coherence, hence falsifiability of the theory. For such a purely mathematical theory the physical connotation must pertain only the interpretation of the mathematics, ranging from the axioms to the final theorems. On the contrary, the postulates of the two current major physical theories either do not have physical interpretation (as for von Neumann’s axioms for quantum theory), or contain physical primitives as ‘clock’, ‘rigid rod’, ‘force’, ‘inertial mass’ (as for special relativity and mechanics). A purely mathematical theory as proposed here, though with limited (but relentlessly growing) domain of applicability, will have the eternal validity of mathematical truth. It will be a theory on which natural sciences can firmly rely. Such kind of theory is what I consider to be the solution of the sixth Hilbert problem. I argue that a prototype example of such a mathematical theory is provided by the novel algorithmic paradigm for physics, as in the recent information-theoretical derivation of quantum theory and free quantum field theory. This article is part of the theme issue ‘Hilbert’s sixth problem’.
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Dissertations / Theses on the topic "Axiomas de Hilbert"

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Portela, Antonio Edilson Cardoso. "Noções de geometria projetiva." reponame:Repositório Institucional da UFC, 2017. http://www.repositorio.ufc.br/handle/riufc/25586.

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PORTELA, Antonio Edilson Cardoso. Noções de geometria projetiva. 2017. 58 f. Dissertação (Mestrado Profissional em Matemática em Rede Nacional) - Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2017.
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Rejected by Rocilda Sales (rocilda@ufc.br), reason: Boa tarde, Estou devolvendo a Dissertação de ANTONIO EDILSON CARDOSO PORTELA, para que o mesmo realize algumas correções na formatação do trabalho. 1- SUMÁRIO ( A formatação do sumário está incorreta, primeiro, retire o último ponto final que aparece após a numeração dos capítulos e seções (Ex.: 3.1. Axioma....; deve ser corrigido para: 3.1 Axioma.....), o alinhamento dos títulos deve seguir o modelo abaixo 1 INTRODUÇÃO.....................00 2 O ESPAÇO...........................00 3 GEOMETRIA........................00 3.1 Axiomas...............................00 REFERÊNCIAS...................00 (OBS.: não altere a formatação do negrito, pois já estava correta) 2- TITULO DOS CAPÍTULOS E SEÇÕES ( retire o ponto final que aparece após o último dígito da numeração dos capítulos e seções, seguindo o modelo do sumário. Retire o recuo de parágrafo dos títulos das seções. Ex.: 3.1 Axioma.......) 3- REFERÊNCIAS ( substitua o termo REFERÊNCIAS BIBLIOGRÁFICAS apenas por REFERÊNCIAS, com fonte n 12, negrito e centralizado. Retire a numeração progressiva que aparece nos itens da referência. Atenciosamente, on 2017-09-06T17:56:50Z (GMT)
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In this work, initially, some results of Linear Algebra are presented, in particular the study of the Vector Space R^n, which becomes, together with Analytical Geometry, the language used in the chapters that follow. We present a study from an axiomatic point of view, from the perspectives of Hilbert's axioms and we elaborate models of planes for the Euclidean, Elliptic and Projective Geometries. The validity of the Incidence and Order axioms for Euclidean Geometry is verified. In R^3, an approach is made to the study of the plane and the unitary sphere, highlighting the elliptical line obtained by the intersection of these sets, thus making an approach to the Elliptic Geometry. With the concepts and definitions studied in the Vector Space R^n, Three-dimensional Space and in the Euclidean and Elliptic Geometries we will approach the study of Projective Geometry, demonstrating propositions and verifying its axioms.
Neste trabalho, inicialmente, apresenta-se alguns resultados da Álgebra Linear, em especial o estudo do Espaço Vetorial R^n, que passa a ser, juntamente com a Geometria Analítica, a linguagem empregada nos capítulos que se seguem. Apresentamos um estudo de um ponto de vista axiomático, sob a ótica dos axiomas de Hilbert e elaboramos modelos de planos para as Geometrias Euclidiana, Elíptica e Projetiva. É verificada a validade dos axiomas de Incidência e Ordem para a Geometria Euclidiana. No R^3, é feita uma abordagem do estudo de plano e da esfera unitária, destacando a reta elíptica obtida pela interseção destes conjuntos, passando assim a fazer uma abordagem da Geometria Elíptica. Com os conceitos e definições estudadas no Espaço Vetorial R^n, Espaço tridimensional e nas Geometrias Euclidiana e Elíptica, abordaremos o estudo da Geometria Projetiva, demonstrando proposições e verificando os seus axiomas.
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SOUZA, Carlos Bino de. "Geometria hiperbólica : consistência do modelo de disco de Poincaré." Universidade Federal Rural de Pernambuco, 2015. http://www.tede2.ufrpe.br:8080/tede2/handle/tede2/6695.

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Euclid wrote a book in 13 volumes called Elements where systematized all the mathematical knowledge of his time. In this work, the 5 postulates of Euclidean geometry were presented. For several years, the 5th Postulate was frequently asked, this inquiries it was discovered that there are several other possible geometries, including hyperbolic geometry. Beltrimi proved that hyperbolic geometry is consistent if Euclidean geometry is consistent. Hilbert showed that Euclidean geometry is consistent if the arithmetic is consistent and presented an axiomatic system that capped the gaps in Euclid’s axiomatic system. Poincaré created a model, called the Poincaré disk, to represent the plan of hyperbolic geometry. The objective of this work is to show that the Poincaré disk model is consistent with reference Axioms Hilbert, replacing only the Axioms of Parallel to "On a point outside a line passes through the two parallel straight lines given", by constructions of Euclidean geometry.
Euclides escreveu uma obra em 13 volumes chamada de Elementos onde sistematizava todo o conhecimento matemático do seu tempo. Nesta obra, foram apresentados os 5 postulados da Geometria Euclidiana. Durante vários anos, o 5o Postulado foi muito questionado, desses questionamentos descobriu-se a existência de várias outras Geometrias possíveis, entre elas a Geometria Hiperbólica. Beltrimi provou que a Geometria Hiperbólica é consistente se a Geometria Euclidiana é consistente. Hilbert mostrou que a Geometria Euclidiana é consistente se a Aritmética é consistente e apresentou um sistema axiomático que preencheu as lacunas do sistema axiomático de Euclides. Poincaré criou um Modelo, chamado de Disco de Poincaré, para representar o plano da Geometria Hiperbólica. O objetivo deste trabalho é mostrar que o Modelo de Disco de poincaré é consistente, tomando como referência os Axiomas de Hilbert, substituindo apenas os Axiomas das Paralelas para "Por um ponto fora de uma reta passam duas retas paralelas à reta dada", através de construções da Geometria Euclidiana.
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Ward, Peter James. "Euclid's Elements, from Hilbert's Axioms." The Ohio State University, 2012. http://rave.ohiolink.edu/etdc/view?acc_num=osu1354311965.

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Books on the topic "Axiomas de Hilbert"

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Ludwig, Günther. An Axiomatic Basis for Quantum Mechanics: Volume 1 Derivation of Hilbert Space Structure. Berlin, Heidelberg: Springer Berlin Heidelberg, 1985.

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Hilbert: : En busca de los axiomas universales. RBA, 2017.

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David Hilbert and the Axiomatization of Physics (1898-1918): From Grundlagen der Geometrie to Grundlagen der Physik (Archimedes). Springer, 2004.

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Rau, Jochen. Quantum Theory. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780199595068.003.0002.

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From the outset statistical mechanics will be framed in the language of quantum theory. The typical macroscopic system is composed of multiple constituents, and hence described in some many-particle Hilbert space. In general, not much is known about such a system, certainly not the precise preparation of all its microscopic details. Thus, its description requires a more general notion of a quantum state, a so-called mixed state. This chapter begins with a brief review of the basic axioms of quantum theory regarding observables, pure states, measurements, and time evolution. Particular attention is paid to the use of projection operators and to the most elementary quantum system, a two-level system. The chapter then motivates the introduction of mixed states and examines in detail their mathematical representation and properties. It also dwells on the description of composite systems, introducing, in particular, the notions of statistical independence and correlations.
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Book chapters on the topic "Axiomas de Hilbert"

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Hartshorne, Robin. "Hilbert’s Axioms." In Undergraduate Texts in Mathematics, 65–116. New York, NY: Springer New York, 2000. http://dx.doi.org/10.1007/978-0-387-22676-7_3.

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Sossinsky, A. "Hilbert’s axioms for plane geometry." In The Student Mathematical Library, 271–82. Providence, Rhode Island: American Mathematical Society, 2012. http://dx.doi.org/10.1090/stml/064/19.

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Anglin, W. S., and J. Lambek. "Non-Euclidean Geometry and Hilbert’s Axioms." In The Heritage of Thales, 89–92. New York, NY: Springer New York, 1995. http://dx.doi.org/10.1007/978-1-4612-0803-7_18.

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Schuster, Peter, and Daniel Wessel. "Syntax for Semantics: Krull’s Maximal Ideal Theorem." In Paul Lorenzen -- Mathematician and Logician, 77–102. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-65824-3_6.

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AbstractKrull’s Maximal Ideal Theorem (MIT) is one of the most prominent incarnations of the Axiom of Choice (AC) in ring theory. For many a consequence of AC, constructive counterparts are well within reach, provided attention is turned to the syntactical underpinning of the problem at hand. This is one of the viewpoints of the revised Hilbert Programme in commutative algebra, which will here be carried out for MIT and several related classical principles.
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Lellmann, Björn, and Dirk Pattinson. "Correspondence between Modal Hilbert Axioms and Sequent Rules with an Application to S5." In Lecture Notes in Computer Science, 219–33. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-40537-2_19.

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Brading, Katherine A., and Thomas A. Ryckman. "Hilbert’s Axiomatic Method and His “Foundations of Physics”: Reconciling Causality with the Axiom of General Invariance." In Einstein and the Changing Worldviews of Physics, 175–99. Boston: Birkhäuser Boston, 2011. http://dx.doi.org/10.1007/978-0-8176-4940-1_8.

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Dasgupta, Subrata. "Entscheidungsproblem: What’s in a Word?" In It Began with Babbage. Oxford University Press, 2014. http://dx.doi.org/10.1093/oso/9780199309412.003.0008.

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In 1900, the celebrated German mathematician David Hilbert (1862–1943), professor of mathematics in the University of Göttingen, delivered a lecture at the International Mathematics Congress in Paris in which he listed 23 significant “open” (mathematicians’ jargon for “unsolved”) problems in mathematics. Hilbert’s second problem was: Can it be proved that the axioms of arithmetic are consistent? That is, that theorems in arithmetic, derived from these axioms, can never lead to contradictory results? To appreciate what Hilbert was asking, we must understand that in the fin de siècle world of mathematics, the “axiomatic approach” held sway over mathematical thinking. This is the idea that any branch of mathematics must begin with a small set of assumptions, propositions, or axioms that are accepted as true without proof. Armed with these axioms and using certain rules of deduction, all the propositions concerning that branch of mathematics can be derived as theorems. The sequence of logically derived steps leading from axioms to theorems is, of course, a proof of that theorem. The axioms form the foundation of that mathematical system. The axiomatic development of plane geometry, going back to Euclid of Alexandria (fl . 300 BCE ) is the oldest and most impressive instance of the axiomatic method, and it became a model of not only how mathematics should be done, but also of science itself. Hilbert himself, in 1898 to 1899, wrote a small volume titled Grundlagen der Geometrie (Foundations of Geometry) that would exert a major influence on 20th-century mathematics. Euclid’s great work on plane geometry, Elements, was axiomatic no doubt, but was not axiomatic enough. There were hidden assumptions, logical problems, meaningless definitions, and so on. Hilbert’s treatment of geometry began with three undefined objects—point, line, and plane—and six undefined relations, such as being parallel and being between. In place of Euclid’s five axioms, Hilbert postulated a set of 21 axioms. In fact, by Hilbert’s time, mathematicians were applying the axiomatic approach to entire branches of mathematics.
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von Plato, Jan. "The Göttingers." In The Great Formal Machinery Works. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691174174.003.0008.

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This chapter studies how around 1918, when work based on Bertrand Russell began in Göttingen, Russell's axioms with disjunction and negation as primitives were used. By the mid-1920s, David Hilbert and others in Göttingen gave axiomatizations for all the standard connectives separately. The motivation for the connectives was the same as in axiomatic studies in geometry: to separate the role of the basic notions, especially negation. This move proved its worth when the axioms of intuitionistic logic were figured out, as in Arend Heyting (1930). Paul Bernays had in fact found the right axioms already in 1925, as he wrote in a letter to Heyting (found in Troelstra 1990).
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9

"Hilbert’s axioms for plane Euclidean geometry." In Geometry: The Line and the Circle, 461–62. Providence, Rhode Island: American Mathematical Society, 2018. http://dx.doi.org/10.1090/text/044/21.

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10

"C. Hilbert’s Axioms for Euclidean Plane Geometry." In AMS/MAA Textbooks, 499–502. Providence, Rhode Island: American Mathematical Society, 2015. http://dx.doi.org/10.1090/text/026/14.

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Conference papers on the topic "Axiomas de Hilbert"

1

Navarro, Juan F. "EL ARTE COMO AXIOMA DEL ARTE." In III Congreso Internacional de Investigación en Artes Visuales :: ANIAV 2017 :: GLOCAL. Valencia: Universitat Politècnica València, 2017. http://dx.doi.org/10.4995/aniav.2017.4617.

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Abstract:
Desde que las primeras mujeres comenzaron a representar escenas de caza en las paredes de las cuevas, el Arte se ha valido de los métodos y procesos de la Ciencia. En la postmodernidad, su discurso se ha vuelto cada vez más complejo, autorreferencial y, en cierto sentido, axiomático: el Arte se presenta como un axioma del Arte. Expresado en términos análogos a los planteados en el teorema de incompletitud de Gödel, podemos afirmar que hay proposiciones del sistema del Arte que no son decidibles dentro del propio sistema. El objeto de AXIOMA es construir una teoría axiomática del sistema del Arte basada en la formulación de Zermelo-Fraenkel. Tal sistema queda definido por su lenguaje, sistema de axiomas y sistema lógico. El lenguaje está formado por términos, que designan objetos del sistema, y fórmulas, que representan aserciones sobre estos objetos. El sistema lógico permite inferir proposiciones y, en un principio, lo asumiremos dado de modo intuitivo. En realidad, AXIOMA es un imposible, como lo fue el programa de Hilbert. La meta de este programa era encontrar un conjunto de axiomas para la aritmética que cumpliera las cuatro propiedades siguientes: (1) Consistencia: no puede demostrarse un enunciado y su negación a partir de los axiomas. (2) La validez de cualquier demostración basada en esos axiomas debe ser verificable en un número finito de pasos. (3) Cualquier enunciado o su contrario debe ser demostrable a partir de los axiomas. (4) La consistencia de los axiomas debe ser verificable en un número finito de pasos. El primer teorema de incompletitud de Gödel establece que si se cumplen (1) y (2), entonces (3) nunca puede cumplirse. Aunque AXIOMA es un proyecto abocado al fracaso, esperamos que sirva para arrojar algo de luz sobre algunas afirmaciones en relación al sistema del Arte.http://dx.doi.org/10.4995/ANIAV.2017.4617
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2

D’Ariano, Giacomo Mauro. "How to Derive the Hilbert-Space Formulation of Quantum Mechanics From Purely Operational Axioms." In QUANTUM MECHANICS: Are There Quantum Jumps? - and On the Present Status of Quantum Mechanics. AIP, 2006. http://dx.doi.org/10.1063/1.2219356.

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