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- W3216167597 abstract "The thin set theorem for n-tuples and k colors ( ) states that every k-coloring of admits an infinite set of integers H such that avoids at least one color. In this paper, we study the combinatorial weakness of the thin set theorem in reverse mathematics by proving neither , nor the free set theorem ( ) imply the Erdős–Moser theorem ( ) whenever k is sufficiently large (answering a question of Patey and giving a partial result towards a question of Cholak Giusto, Hirst and Jockusch). Given a problem , a computable instance of is universal iff its solution computes a solution of any other computable -instance. It has been established that most of Ramsey-type problems do not have a universal instance, but the case of Erdős–Moser theorem remained open so far. We prove that Erdős–Moser theorem does not admit a universal instance (answering a question of Patey)." @default.
- W3216167597 created "2021-12-06" @default.
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- W3216167597 date "2021-11-24" @default.
- W3216167597 modified "2023-10-17" @default.
- W3216167597 title "THE REVERSE MATHEMATICS OF THE THIN SET AND ERDŐS-MOSER THEOREMS" @default.
- W3216167597 doi "https://doi.org/10.1017/jsl.2021.98" @default.
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