The Sacks density theorem and Σ2-bounding

Journal of Symbolic Logic 61 (2):450 - 467 (1996)

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 - + BΣ 2 . The proof has two components: a lemma that in any model of P - + BΣ 2 , if B is recursively enumerable and incomplete then IΣ 1 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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References found in this work

The Α-Finite Injury Method.G. E. Sacks & S. G. Simpson - 1972 - Annals of Mathematical Logic 4 (4):343-367.
Finite Injury and Σ1-Induction.Michael Mytilinaios - 1989 - Journal of Symbolic Logic 54 (1):38 - 49.
The Alpha-Finite Injury Method.G. E. Sacks - 1972 - Annals of Mathematical Logic 4 (4):343.
The Recursively Enumerable Degrees Are Dense.Gerald E. Sacks - 1969 - Journal of Symbolic Logic 34 (2):294-295.

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Citations of this work

∑2-Constructions and I∑1.Marcia Groszek & Tamara Hummel - 1998 - Annals of Pure and Applied Logic 93 (1-3):83-101.
∑< Sub> 2-Constructions and< I> I_∑< Sub> 1.Marcia Groszek & Tamara Hummel - 1998 - Annals of Pure and Applied Logic 93 (1):83-101.
∑2-Constructions and I∑1.Marcia Groszek & Tamara Hummel - 1998 - Annals of Pure and Applied Logic 93 (1):83-101.
Coding a Family of Sets.J. F. Knight - 1998 - Annals of Pure and Applied Logic 94 (1-3):127-142.

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