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The Sacks density theorem and Σ2-bounding

Published online by Cambridge University Press:  12 March 2014

Marcia J. Groszek ,
Michael E. Mytilinaios  and
Theodore A. Slaman
Marcia J. Groszek
Affiliation:
Department of Mathematics, Dartmouth College, Hanover New Hampshire 03755, USA, E-mail: Marcia.Groszek@dartmouth.edu
Michael E. Mytilinaios
Affiliation:
Department of Informatics, Athens University of Economics, Patission 76, Athens 104 34, Greece, E-mail: mmit@isosun.ariadne-t.gr
Theodore A. Slaman
Affiliation:
Department of Mathematics, The University of Chicago, Chicago, Illinois 60637, USA, E-mail: ted@math.uchicago.edu
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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.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 61 , Issue 2 , June 1996 , pp. 450 - 467
Copyright
Copyright © Association for Symbolic Logic 1996

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References

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