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Models of arithmetic and upper bounds for arithmetic sets

Published online by Cambridge University Press:  12 March 2014

Alistair H. Lachlan  and
Robert I. Soare
Alistair H. Lachlan
Affiliation:
Department of Mathematics and Statistics, Simon Fraser University, Burnaby, British Columbia, CanadaV5A 1S6, E-mail: alistair@sfu.ca
Robert I. Soare
Affiliation:
Department of Mathematics, University of Chicago, Chicago, Illinois 60637, E-mail: soare@math.uchicago.edu
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Abstract

We settle a question in the literature about degrees of models of true arithmetic and upper bounds for the arithmetic sets. We prove that there is a model of true arithmetic whose degree is not a uniform upper bound for the arithmetic sets. The proof involves two forcing constructions.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 59 , Issue 3 , September 1994 , pp. 977 - 983
Copyright
Copyright © Association for Symbolic Logic 1994

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References

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