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  1. On the Strength of Ramsey's Theorem.David Seetapun & Theodore A. Slaman - 1995 - Notre Dame Journal of Formal Logic 36 (4):570-582.
    We show that, for every partition F of the pairs of natural numbers and for every set C, if C is not recursive in F then there is an infinite set H, such that H is homogeneous for F and C is not recursive in H. We conclude that the formal statement of Ramsey's Theorem for Pairs is not strong enough to prove , the comprehension scheme for arithmetical formulas, within the base theory , the comprehension scheme for recursive formulas. (...)
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  • (1 other version)Formalizing forcing arguments in subsystems of second-order arithmetic.Jeremy Avigad - 1996 - Annals of Pure and Applied Logic 82 (2):165-191.
    We show that certain model-theoretic forcing arguments involving subsystems of second-order arithmetic can be formalized in the base theory, thereby converting them to effective proof-theoretic arguments. We use this method to sharpen the conservation theorems of Harrington and Brown-Simpson, giving an effective proof that WKL+0 is conservative over RCA0 with no significant increase in the lengths of proofs.
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  • (1 other version)Classical Recursion Theory.Peter G. Hinman - 2001 - Bulletin of Symbolic Logic 7 (1):71-73.
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  • Correction to “a cohesive set which is not high”.Carl Jockusch & Frank Stephan - 1997 - Mathematical Logic Quarterly 43 (4):569-569.
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  • A cohesive set which is not high.Carl Jockusch & Frank Stephan - 1993 - Mathematical Logic Quarterly 39 (1):515-530.
    We study the degrees of unsolvability of sets which are cohesive . We answer a question raised by the first author in 1972 by showing that there is a cohesive set A whose degree a satisfies a' = 0″ and hence is not high. We characterize the jumps of the degrees of r-cohesive sets, and we show that the degrees of r-cohesive sets coincide with those of the cohesive sets. We obtain analogous results for strongly hyperimmune and strongly hyperhyperimmune sets (...)
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