PARTITION GENERICITY AND PIGEONHOLE BASIS THEOREMS
نویسندگان
چکیده
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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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Let A = (ai,j) , i = 1, 2, . . . , j = 0, 1, 2, . . . , be an infinite matrix with elements ai,j = 0 or 1; p (n, k;A) the number of partitions of n into k parts whose number yi of parts which are equal to i belongs to the set Yi = {j : ai,j = 1} , i = 1, 2, . . . . The universal theorem on partitions states that 1 X n=0 n X k=0 p (n, k;A)ut = 1 Y i=1 0 @ 1 X j=0 ai,ju t 1 A . In this paper, we ...
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The computability-theoretic and reverse mathematical aspects of various combinatorial principles, such as König’s Lemma and Ramsey’s Theorem, have received a great deal of attention and are active areas of research. We carry on this study of effective combinatorics by analyzing various partition theorems (such as Ramsey’s Theorem) with the aim of understanding the complexity of solutions to com...
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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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ژورنال
عنوان ژورنال: Journal of Symbolic Logic
سال: 2022
ISSN: ['1943-5886', '0022-4812']
DOI: https://doi.org/10.1017/jsl.2022.69