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On expandability of models of Peano arithmetic to models of the alternative set theory

Published online by Cambridge University Press:  12 March 2014

Athanassios Tzouvaras
Athanassios Tzouvaras*
Affiliation:
Department of Mathematics, University of Thessaloniki, 540 06 Thessaloniki, Greece, E-mail: cbbz04@grtheunl.bitnet
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Abstract

We give a sufficient condition for a countable model M of PA to be expandable to an ω-model of AST with absolute Ω-orderings. The condition is in terms of saturation schemes or, equivalently, in terms of the ability of the model to code sequences which have some kind of definition in (M, ω). We also show that a weaker scheme of saturation leads to the existence of wellorderings of the model with nice properties. Finally, we answer affirmatively the question of whether the intersection of all β-expansions of a β-expandable model M is the set RA(M, ω)—the ramified analytical hierarchy over (M, ω).

The results are based on forcing constructions.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 57 , Issue 2 , June 1992 , pp. 452 - 460
Copyright
Copyright © Association for Symbolic Logic 1992

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References

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