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The Sacks density theorem and Σ2-bounding
Published online by Cambridge University Press: 12 March 2014
Abstract
The Sacks Density Theorem [7] states that the Turing degrees of the recursively enumerable sets are dense. We show that the Density Theorem holds in every model of P− + BΣ2. The proof has two components: a lemma that in any model of P− + BΣ2, if B is recursively enumerable and incomplete then IΣ1 holds relative to B and an adaptation of Shore's [9] blocking technique in α-recursion theory to models of arithmetic.
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- Copyright © Association for Symbolic Logic 1996
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