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Steen Lempp 2
"... We construct the set of the title, answering a question of Cholak, Jockusch, and Slaman [1], and discuss its connections with the study of the proof-theoretic strength and eective content of versions of Ramsey's Theorem. ..."
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We construct the set of the title, answering a question of Cholak, Jockusch, and Slaman [1], and discuss its connections with the study of the proof-theoretic strength and eective content of versions of Ramsey's Theorem.
On Turing Reducibility
, 1994
"... We show that the transitivity of pointwise Turing reducibility on the recursively enumerable sets of integers cannot be proven in P - + I# 1 , first order arithmetic with induction limited to # 1 predicates. We produce a example of intransitivity in a nonstandard model of P - +I# 1 by a finite in ..."
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We show that the transitivity of pointwise Turing reducibility on the recursively enumerable sets of integers cannot be proven in P - + I# 1 , first order arithmetic with induction limited to # 1 predicates. We produce a example of intransitivity in a nonstandard model of P - +I# 1 by a finite injury priority construction.
