Add to ORKGAbstract. We study the reverse mathematics and computability-the-oretic strength of (stable) Ramsey’s Theorem for pairs and the related principles COH and DNR. We show that SRT22 implies DNR over RCA0 but COH does not, and answer a question of Mileti by showing that every computable stable 2-coloring of pairs has an incomplete ∆02 infinite homogeneous set. We also give some extensions of the latter result, and relate it to potential approaches to showing that SRT22 does not imply RT22. 1
21 pagesInternational audienceWe complete a 40-year old program on the computability-theoretic analy...
We characterize the effective content and the proof-theoretic strength of a Ramsey-type theorem for ...
Abstract. We discuss the use of nonstandard methods in the study of Ramsey type problems, and illust...
Abstract. We study the reverse mathematics and computability-the-oretic strength of (stable) Ramsey’...
We study the reverse mathematics and computability-theoretic strength of (stable) Ramsey’s Theorem f...
International audienceWe answer a question posed by Hirschfeldt and Jockusch by showing that wheneve...
he main objective of this research is to study the relative strength of combinatorial principles, in...
Abstract. We show that the principle PART from Hirschfeldt and Shore [7] is equivalent to the Σ02-Bo...
International audienceRamsey's theorem for n-tuples and k-colors (RT n k) asserts that every k-color...
The computability-theoretic and reverse mathematical aspects of various combinatorial principles, su...
International audienceRamsey's theorem for pairs asserts that every 2-coloring of the pairs of integ...
Abstract. Ramsey’s theorem states that each coloring has an infinite homo-geneous set, but these set...
31 pagesThe rainbow Ramsey theorem states that every coloring of tuples where each color is used a b...
Abstract. The Rainbow Ramsey Theorem is essentially an “anti-Ramsey ” theorem which states that cert...
International audienceThe tree theorem for pairs (TT 2 2), first introduced by Chubb, Hirst, and McN...
21 pagesInternational audienceWe complete a 40-year old program on the computability-theoretic analy...
We characterize the effective content and the proof-theoretic strength of a Ramsey-type theorem for ...
Abstract. We discuss the use of nonstandard methods in the study of Ramsey type problems, and illust...
Abstract. We study the reverse mathematics and computability-the-oretic strength of (stable) Ramsey’...
We study the reverse mathematics and computability-theoretic strength of (stable) Ramsey’s Theorem f...
International audienceWe answer a question posed by Hirschfeldt and Jockusch by showing that wheneve...
he main objective of this research is to study the relative strength of combinatorial principles, in...
Abstract. We show that the principle PART from Hirschfeldt and Shore [7] is equivalent to the Σ02-Bo...
International audienceRamsey's theorem for n-tuples and k-colors (RT n k) asserts that every k-color...
The computability-theoretic and reverse mathematical aspects of various combinatorial principles, su...
International audienceRamsey's theorem for pairs asserts that every 2-coloring of the pairs of integ...
Abstract. Ramsey’s theorem states that each coloring has an infinite homo-geneous set, but these set...
31 pagesThe rainbow Ramsey theorem states that every coloring of tuples where each color is used a b...
Abstract. The Rainbow Ramsey Theorem is essentially an “anti-Ramsey ” theorem which states that cert...
International audienceThe tree theorem for pairs (TT 2 2), first introduced by Chubb, Hirst, and McN...
21 pagesInternational audienceWe complete a 40-year old program on the computability-theoretic analy...
We characterize the effective content and the proof-theoretic strength of a Ramsey-type theorem for ...
Abstract. We discuss the use of nonstandard methods in the study of Ramsey type problems, and illust...