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Models of arithmetic and subuniform bounds for the 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 60637-1546, USA, E-mail: soare@math.uchicago.edu
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Abstract

It has been known for more than thirty years that the degree of a non-standard model of true arithmetic is a subuniform upper bound for the arithmetic sets (suub). Here a notion of generic enumeration is presented with the property that the degree of such an enumeration is an suub but not the degree of a non-standard model of true arithmetic. This answers a question posed in the literature.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 63 , Issue 1 , March 1998 , pp. 59 - 72
Copyright
Copyright © Association for Symbolic Logic 1998

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References

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