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- W2143608087 abstract "The infinite Ramsey theorem is known to be equivalent to the statement ‘for every set X and natural number n, the n-th Turing jump of X exists', over RCA0 due to results of Jockusch [5]. By subjecting the theory RCA0 augmented by the latter statement to an ordinal analysis, we give a direct proof of the fact that the infinite Ramsey theorem has proof-theoretic strength eω. The upper bound is obtained by means of cut elimination and the lower bound by extending the standard well-ordering proofs for ACA0. There is a proof of this result due to McAloon [6], using model-theoretic and combinatorial techniques. According to [6], another proof appeared in an unpublished paper by Jager." @default.
- W2143608087 created "2016-06-24" @default.
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- W2143608087 date "2012-01-01" @default.
- W2143608087 modified "2023-09-28" @default.
- W2143608087 title "Ordinal Analysis and the Infinite Ramsey Theorem" @default.
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- W2143608087 doi "https://doi.org/10.1007/978-3-642-30870-3_1" @default.
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