Results 1 to 10 of about 1,125 (159)
Landauer Principle and Einstein Synchronization of Clocks: Ramsey Approach. [PDF]
Entropy (Basel)We introduce a synchronization procedure for clocks based on the Einstein–Landauer framework. Clocks are modeled as discrete, macroscopic devices operating at a thermal equilibrium temperature T.
Bormashenko E, Nosonovsky M.
europepmc +2 more sources
Two extensions of Ramsey's theorem [PDF]
Duke Mathematical Journal, 2012 Ramsey's theorem, in the version of Erd\H{o}s and Szekeres, states that every 2-coloring of the edges of the complete graph on {1, 2,...,n} contains a monochromatic clique of order 1/2\log n.
Conlon, David +2 more
core +8 more sources
The proof-theoretic strength of Ramsey's theorem for pairs and two colors [PDF]
, 2018 Ramsey's theorem for $n$-tuples and $k$-colors ($\mathsf{RT}^n_k$) asserts that every k-coloring of $[\mathbb{N}]^n$ admits an infinite monochromatic subset.
Ludovic Patey, Keita Yokoyama
openalex +7 more sources
Formalized Mathematics, 2008 Summary. The goal of this article is to formalize two versions of Ramsey’s theorem. The theorems are not phrased in the usually pictorial representation of a coloured graph but use a set-theoretic terminology. After some useful lemma, the second section presents a generalization of Ramsey’s theorem on infinite set closely following the book [9].
Marco Riccardi
openalex +3 more sources
Stable Ramsey's Theorem and Measure [PDF]
Notre Dame Journal of Formal Logic, 2010 The stable Ramsey's theorem for pairs has been the subject of numerous investigations in mathematical logic. We introduce a weaker form of it by restricting from the class of all stable colorings to subclasses of it that are non-null in a certain effective measure-theoretic sense. We show that the sets that can compute infinite homogeneous sets for non-
Damir D. Dzhafarov
+7 more sources
Is Ramsey's Theorem omega-automatic?
, 2010 We study the existence of infinite cliques in omega-automatic (hyper-)graphs. It turns out that the situation is much nicer than in general uncountable graphs, but not as nice as for automatic graphs.
Dietrich Kuske
openalex +4 more sources
An Application of Ramsey's Theorem [PDF]
Canadian Mathematical Bulletin, 1970 By an r-graph, we mean a finite set V of elements called vertices and a collection of some of the r-subsets of V called edges with the property that each vertex is incident with at least one edge. An A-chromatic r-graph is an r-graph all of whose edges are coloured A.Theorem. Let G1, …, Gt denote r-graphs.
E. J. Cockayne
openalex +3 more sources
Is Ramsey's theorem omega-automatic? [PDF]
, 2009 We study the existence of infinite cliques in omega-automatic (hyper-)graphs. It turns out that the situation is much nicer than in general uncountable graphs, but not as nice as for automatic graphs. More specifically, we show that every uncountable omega-automatic graph contains an uncountable co-context-free clique or anticlique, but not necessarily
Dietrich Kuske
openalex +6 more sources
Ramsey's Theorem for a Class of Categories. [PDF]
Proc Natl Acad Sci U S A, 1972 Graham RL, Leeb K, Rothschild BL.
europepmc +3 more sources
A Note on Ramsey's Theorem [PDF]
Canadian Mathematical Bulletin, 1972 H. L. Abbott
openalex +3 more sources