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A note on standard systems and ultrafilters

Published online by Cambridge University Press:  12 March 2014

Fredrik Engström*
Affiliation:
Department of Philosophy, Göteborg UniversityBox 200, 405 30 Göteborg, Sweden, E-mail: fredrik.engstrom@filosofi.gu.se

Abstract

Let (M, )⊨ ACA0 be such that , the collection of all unbounded sets in , admits a definable complete ultrafilter and let T be a theory extending first order arithmetic coded in such that M thinks T is consistent. We prove that there is an end-extension NT of M such that the subsets of M coded in N are precisely those in . As a special case we get that any Scott set with a definable ultrafilter coding a consistent theory T extending first order arithmetic is the standard system of a recursively saturated model of T.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 2008

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References

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