Results 11 to 20 of about 1,125 (159)
The logical strength of B\"uchi's decidability theorem [PDF]
Logical Methods in Computer Science, 2019 We study the strength of axioms needed to prove various results related to automata on infinite words and B\"uchi's theorem on the decidability of the MSO theory of $(N, {\le})$.
Leszek Kołodziejczyk +3 more
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Using Ramsey’s theorem once [PDF]
Archive for Mathematical Logic, 2019 We show that RT(2,4) cannot be proved with one typical application of RT(2,2) in an intuitionistic extension of RCA0 to higher types, but that this does not remain true when the law of the excluded middle is added. The argument uses Kohlenbach's axiomatization of higher order reverse mathematics, results related to modified reducibility, and a ...
Jeffry L. Hirst, Carl Mummert
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Separation Property for wB- and wS-regular Languages [PDF]
Logical Methods in Computer Science, 2014 In this paper we show that {\omega}B- and {\omega}S-regular languages satisfy the following separation-type theorem If L1,L2 are disjoint languages of {\omega}-words both recognised by {\omega}B- (resp.
Michał Skrzypczak
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Turán and Ramsey problems for alternating multilinear maps
Discrete Analysis, 2023 Turán and Ramsey problems for alternating multilinear maps, Discrete Analysis 2023:12, 22 pp. Ramsey's theorem (in its finite version) states that for every positive integer $k$ there exists a positive integer $n$ such that every graph with $n$ vertices
Youming Qiao
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Open questions about Ramsey-type statements in reverse mathematics [PDF]
, 2015 Ramsey's theorem states that for any coloring of the n-element subsets of N with finitely many colors, there is an infinite set H such that all n-element subsets of H have the same color.
Patey, Ludovic
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Ramsey’s theorem for spaces [PDF]
Transactions of the American Mathematical Society, 1979 A short proof is given of the following known result. For all k, r, t there exists n so that if the t-spaces of an n-space are r-colored there exists a k-space all of whose t-spaces are the same color. Here t-space refers initially to a t-dimensional affine space over a fixed finite field. The result is also shown for a more general notion of t-space.
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The weakness of being cohesive, thin or free in reverse mathematics [PDF]
, 2016 Informally, a mathematical statement is robust if its strength is left unchanged under variations of the statement. In this paper, we investigate the lack of robustness of Ramsey's theorem and its consequence under the frameworks of reverse mathematics ...
Patey, Ludovic
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Reverse mathematics and infinite traceable graphs [PDF]
, 2010 This paper falls within the general program of investigating the proof theoretic strength (in terms of reverse mathematics) of combinatorial principals which follow from versions of Ramsey's theorem.
Cholak, Peter +2 more
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Controlling iterated jumps of solutions to combinatorial problems [PDF]
, 2016 Among the Ramsey-type hierarchies, namely, Ramsey's theorem, the free set, the thin set and the rainbow Ramsey theorem, only Ramsey's theorem is known to collapse in reverse mathematics.
Patey, Ludovic
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On a topological Ramsey theorem [PDF]
Canadian Mathematical Bulletin, 2022 AbstractWe introduce natural strengthenings of sequential compactness, the r-Ramsey property for each natural number $r\geq 1$ . We prove that metrizable compact spaces are r-Ramsey for all r and give examples of compact spaces that are r-Ramsey but not $(r+1)$ -Ramsey for each $r\geq 1$ (assuming Continuum Hypothesis (CH) for all $r>1 ...
Wiesław Kubiś, Paul Szeptycki
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