منابع مشابه
Partition Theorems and Computability Theory
The connections between mathematical logic and combinatorics have a rich history. This paper focuses on one aspect of this relationship: understanding the strength, measured using the tools of computability theory and reverse mathematics, of various partition theorems. To set the stage, recall two of the most fundamental combinatorial principles, König’s Lemma and Ramsey’s Theorem. We denote th...
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1. INTRODUCTION II [1] two of us iivestigated the problem of determiiiig those cardiials a, /3, y, 8, A for which the followiig statemeet, abbreviated Iá(8, g, a, A, y), holds : "Wheeever V is aa a-dimeesiooal vector space over a field of A elemeets, aad the 8-dimeesiooal subspaces of V are partitiooed iito y classes, there is some /-dimeesiooal subspace of V all of whose 8-dimee-siooal subspac...
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A canonical (i.e., unrestricted) version of the partition theorem for k-parameter sets of Graham and Rothschild (Trans. Amer. Math. Sot. 159 (1971), 257-291) is proven. Some applications, e.g., canonical versions. of the Rado-Folkman-Sanders theorem and of the partition theorem for finite Boolean algebras are given. Also the ErdBs-Rado canonization theorem (J. London Math. Sot. 25 (1950), 249-2...
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We introduce the notions of layered semigroups and partial semigroups, and prove some Ramsey type partition results about them. These results generalize previous results of Gowers [5, Theorem 1], of Furstenberg [3, Proposition 8.21], and of Bergelson, Blass, and Hindman [1, Theorem 4.1]. We give some applications of these results (see e.g., Theorem 1.1), and present examples suggesting that our...
متن کاملPartition Theorems for Spaces of Variable Words
Furstenberg and Katznelson applied methods of topological dynamics to Ramsey theory, obtaining a density version of the Hales-Jewett partition theorem. Inspired by their methods, but using spaces of ultrafilters instead of their metric spaces, we prove a generalization of a theorem of Carlson about variable words. We extend this result to partitions of finite or infinite sequences of variable w...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 1982
ISSN: 0097-3165
DOI: 10.1016/0097-3165(82)90022-x