Relevant bibliographies by topics / Open Coloring Axiom (OCA)

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  1. Journal articles
  2. Dissertations / Theses
  3. Book chapters

Academic literature on the topic 'Open Coloring Axiom (OCA)'

Author: Grafiati
Published: 4 June 2021
Last updated: 18 February 2022

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Journal articles on the topic "Open Coloring Axiom (OCA)"

1

Farah, Ilijas. "Completely Additive Liftings." Bulletin of Symbolic Logic 4, no. 1 (1998): 37–54. http://dx.doi.org/10.2307/421005.

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The purpose of this communication is to survey a theory of liftings, as developed in author's thesis ([8]). The first result in this area was Shelah's construction of a model of set theory in which every automorphism of P(ℕ)/ Fin, where Fin is the ideal of finite sets, is trivial, or inother words, it is induced by a function mapping integers into integers ([33]). (It is a classical result of W. Rudin [31] that under the Continuum Hypothesis there are automorphisms other than trivial ones.) Soon afterwards, Velickovic ([47]), was able to extract from Shelah's argument the fact that every autom
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2

Geschke, Stefan. "A dual open coloring axiom." Annals of Pure and Applied Logic 140, no. 1-3 (2006): 40–51. http://dx.doi.org/10.1016/j.apal.2005.09.003.

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He, Bin. "A high dimensional Open Coloring Axiom." MLQ 51, no. 5 (2005): 462–69. http://dx.doi.org/10.1002/malq.200510003.

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PATEY, LUDOVIC. "THE STRENGTH OF THE TREE THEOREM FOR PAIRS IN REVERSE MATHEMATICS." Journal of Symbolic Logic 81, no. 4 (2016): 1481–99. http://dx.doi.org/10.1017/jsl.2015.80.

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AbstractNo natural principle is currently known to be strictly between the arithmetic comprehension axiom (ACA0) and Ramsey’s theorem for pairs ($RT_2^2$) in reverse mathematics. The tree theorem for pairs ($TT_2^2$) is however a good candidate. The tree theorem states that for every finite coloring over tuples of comparable nodes in the full binary tree, there is a monochromatic subtree isomorphic to the full tree. The principle $TT_2^2$ is known to lie between ACA0 and $RT_2^2$ over RCA0, but its exact strength remains open. In this paper, we prove that $RT_2^2$ together with weak König’s le
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5

Freiling, Chris, and T. H. Payne. "Some properties of large filters." Journal of Symbolic Logic 53, no. 4 (1988): 1027–35. http://dx.doi.org/10.1017/s0022481200027900.

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Dowker [1] raised the question of the existence of filters such that for every coloring (partition) of the underlying index set I with two colors there is a relation R on I which (i) is fat (in the sense that sets of the form {y Є I∣xRy} are in the filter) and (ii) has no bichromatic symmetric pairs (i.e., distinct indices x and y such that x R y and y R x). Additionally, he required that the filter have no anti-symmetric fat relation, for such a relation would vacuously satisfy (i) and (ii). The question of the existence of Dowker filters has been studied more recently by Rudin [3], [4], who
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6

Moore, Justin Tatch. "Some remarks on the Open Coloring Axiom." Annals of Pure and Applied Logic, October 2020, 102912. http://dx.doi.org/10.1016/j.apal.2020.102912.

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Dissertations / Theses on the topic "Open Coloring Axiom (OCA)"

1

Rodríguez, Porras Cristóbal. "Une analyse ensembliste des opérateurs sur l'espace de Banach l_infty/c-0." Sorbonne Paris Cité, 2015. http://www.theses.fr/2015USPCC258.

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On étudie des opérateurs linéaires et continus sur l'espace X=l_infty/c_O et des espaces liés. On commence par examiner des opérateurs T:X → X. On s'intéresse à la possibilité de représenter ses fragments de la forme T_{B,A}:l_infty(A)/c_0(A)→, l_infty(B)/c_0(B), pour A,B C̱ N infinis, par des applications de l_infty(A) dans l_infty(B), des matrices AxB, des fonctions continues de B^*=βB\B dans A^ *, ou des bijections de B dans A. On montre plusieurs exemples. On définit et on étudie de nouvelles classes d'opérateurs. Pour certaines d'entre elles on obtient des représentations satisfactoires.
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Book chapters on the topic "Open Coloring Axiom (OCA)"

1

Velickovic, Boban. "Applications of the Open Coloring Axiom." In Mathematical Sciences Research Institute Publications. Springer US, 1992. http://dx.doi.org/10.1007/978-1-4613-9754-0_12.

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2

"The Open Coloring Axiom." In Forcing for Mathematicians. WORLD SCIENTIFIC, 2014. http://dx.doi.org/10.1142/9789814566018_0026.

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