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A note on Σ1-maximal models

Published online by Cambridge University Press:  12 March 2014

A. Cordón-Franco,
A. Fernández-Margarit and
F.F. Lara-Martín
A. Cordón-Franco
Affiliation:
Dpto. Ciencias de la Computación e Inteligencia Artificial, Facultad de Matemáticas, Universidad de Sevilla, C/ Tarfia, S/N, 41012 Sevilla, Spain, E-mail: acordon@us.es
A. Fernández-Margarit
Affiliation:
Dpto. Ciencias de la Computación e Inteligencia Artificial, Facultad de Matemáticas, Universidad de Sevilla, C/ Tarfia, S/N, 41012 Sevilla, Spain, E-mail: afmargarit@us.es
F.F. Lara-Martín
Affiliation:
Dpto. Ciencias de la Computación e Inteligencia Artificial, Facultad de Matemáticas, Universidad de Sevilla, C/ Tarfia, S/N, 41012 Sevilla, Spain, E-mail: fflara@us.es
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Abstract

Let T be a recursive theory in the language of first order Arithmetic. We prove that if T extends: (a) the scheme of parameter free Δ1-minimization (plus exp). or (b) the scheme of parameter free Π1-induction, then there are no Σ1-maximal models with respect to T. As a consequence, we obtain a new proof of an unpublished theorem of Jeff Paris stating that Σ1-maximal models with respect to IΔ0 + exp do not satisfy the scheme of Σ1-collection BΣ1.

Information

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 72 , Issue 3 , September 2007, pp. 1072 - 1078
Copyright
Copyright © Association for Symbolic Logic 2007

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References

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