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• W2292597986 abstract "In this thesis, we investigate the computational content and the logical strength of Ramsey's theorem and its consequences. For this, we use the frameworks of reverse mathematics and of computable reducibility. We proceed to a systematic study of various Ramsey-type statements under a unified and minimalistic framework and obtain a precise analysis of their interrelations. We clarify the role of the number of colors in Ramsey's theorem. In particular, we show that the hierarchy of Ramsey's theorem induced by the number of colors is strictly increasing over computable reducibility, and exhibit in reverse mathematics an infinite decreasing hiearchy of Ramsey-type theorems by weakening the homogeneity constraints. These results tend to show that the Ramsey-type statements are not robust, that is, slight variations of the statements lead to strictly different subsystems. Finally, we pursuit the analysis of the links between Ramsey's theorems and compacity arguments, by extending Liu's theorem to several Ramsey-type statements and by proving its optimality under various aspects." @default.
• W2292597986 created "2016-06-24" @default.
• W2292597986 creator A5032131260 @default.
• W2292597986 date "2016-01-18" @default.
• W2292597986 modified "2023-09-27" @default.
• W2292597986 title "The reverse mathematics of Ramsey-type theorems" @default.
• W2292597986 hasPublicationYear "2016" @default.
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