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On the complexity of models of arithmetic

Published online by Cambridge University Press:  12 March 2014

Kenneth McAloon
Kenneth McAloon*
Affiliation:
U.E.R. de Mathematiques, Universite Paris VII, Paris, France
*
Current address: Brooklyn College of C.U.N.Y., Brooklyn, New York, 11210
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Abstract

Let P0 be the subsystem of Peano arithmetic obtained by restricting induction to bounded quantifier formulas. Let M be a countable, nonstandard model of P0 whose domain we suppose to be the standard integers. Let T be a recursively enumerable extension of Peano arithmetic all of whose existential consequences are satisfied in the standard model. Then there is an initial segment M′ of M which is a model of T such that the complete diagram of M′ is Turing reducible to the atomic diagram of M. Moreover, neither the addition nor the multiplication of M is recursive.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 47 , Issue 2 , June 1982 , pp. 403 - 415
Copyright
Copyright © Association for Symbolic Logic 1982

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References

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