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Model-theoretic properties characterizing Peano arithmetic

Published online by Cambridge University Press:  12 March 2014

Richard Kaye
Richard Kaye*
Affiliation:
Jesus College, Oxford OX1 3DW, England
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Abstract

Let = {0,1, +,·,<} be the usual first-order language of arithmetic. We show that Peano arithmetic is the least first-order -theory containing IΔ0 + exp such that every complete extension T of it has a countable model K satisfying

(i) K has no proper elementary substructures, and

(ii) whenever L ≻ K is a countable elementary extension there is and such that .

Other model-theoretic conditions similar to (i) and (ii) are also discussed and shown to characterize Peano arithmetic.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 56 , Issue 3 , September 1991 , pp. 949 - 963
Copyright
Copyright © Association for Symbolic Logic 1991

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