Results 21 to 30 of about 1,125 (159)
Indivisibility and uniform computational strength [PDF]
Logical Methods in Computer ScienceA countable structure is indivisible if for every coloring with finite range there is a monochromatic isomorphic subcopy of the structure. Each indivisible structure naturally corresponds to an indivisibility problem which outputs such a subcopy given a ...
Kenneth Gill
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The polarized Ramsey’s theorem [PDF]
Archive for Mathematical Logic, 2008 The authors study the proof-theoretic strength of a version of Ramsey's theorem called the Polarized Ramsey's Theorem. Given a coloring \(f: [\omega]^n\to k\), a \(p\)-homogeneous set for \(f\) is a sequence \(\langle H_1,\dots,H_n\rangle\) of infinite sets such that for some \(c\), \(f(\langle x_1,\dots,x_n\rangle)=c\) for every tuple \(\langle x_1 ...
Dzhafarov, Damir D., Hirst, Jeffry L.
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Ramsey's Theorem for Pairs and $k$ Colors as a Sub-Classical Principle of Arithmetic [PDF]
, 2016 The purpose is to study the strength of Ramsey's Theorem for pairs restricted to recursive assignments of $k$-many colors, with respect to Intuitionistic Heyting Arithmetic.
Berardi, Stefano, Steila, Silvia
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A sharp threshold for van der Waerden's theorem in random subsets
Discrete Analysis, 2016 A sharp threshold for van der Waerden's theorem in random subsets, Discrete Analysis, 2016:7, 19 pp. In recent years there has been a great deal of progress on problems that arise when one takes a notable combinatorial theorem such as Ramsey's theorem ...
Ehud Friedgut +3 more
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A multidimensional Ramsey Theorem
, 2022 Ramsey theory is a central and active branch of combinatorics. Although Ramsey numbers for graphs have been extensively investigated since Ramsey's work in the 1930s, there is still an exponential gap between the best known lower and upper bounds. For $k$-uniform hypergraphs, the bounds are of tower-type, where the height grows with $k$.
Girao, A, Kronenberg, G, Scott, AD
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A Model Theoretic Proof of Completeness of an Axiomatization of Monadic Second-Order Logic on Streams [PDF]
, 2012 International audienceWe discuss the completeness of an axiomatization of Monadic Second- Order Logic (MSO) on infinite words (or streams). By using model-theoretic tools, we give an alternative proof of D.
Riba, Colin
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On uniform relationships between combinatorial problems [PDF]
, 2015 The enterprise of comparing mathematical theorems according to their logical strength is an active area in mathematical logic, with one of the most common frameworks for doing so being reverse mathematics. In this setting, one investigates which theorems
Dorias, FG +4 more
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Phase transitions related to the pigeonhole principle [PDF]
, 2014 Since Paris introduced them in the late seventies (Paris1978), densities turned out to be useful for studying independence results. Motivated by their simplicity and surprising strength we investigate the combinatorial complexity of two such densities ...
A. Weiermann +4 more
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A Ramsey theorem for multiposets [PDF]
European Journal of Combinatorics, 2019 In the parlance of relational structures, the Finite Ramsey Theorem states that the class of all finite chains has the Ramsey property. A classical result of J. Ne et il and V. R dl claims that the class of all finite posets with a linear extension has the Ramsey property. In 2010 M.
Nemanja Draganić, Dragan Mašulović
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Ideal version of Ramsey’s theorem [PDF]
Czechoslovak Mathematical Journal, 2011 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Filipów, R. +3 more
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