September 2007 A note on Σ1-maximal models
A. Cordón—Franco, F. F. Lara—Martín
J. Symbolic Logic 72(3): 1072-1078 (September 2007). DOI: 10.2178/jsl/1191333857

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free Π1-induction, then there are no Σ1-maximal models with respect to T. As a consequence, we obtain a new proof of an unpublished theorem of Jeff Paris stating that Σ1-maximal models with respect to IΔ0 + exp do not satisfy the scheme of Σ1-collection BΣ1.

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A. Cordón—Franco. F. F. Lara—Martín. "A note on Σ1-maximal models." J. Symbolic Logic 72 (3) 1072 - 1078, September 2007. https://doi.org/10.2178/jsl/1191333857

Information

Published: September 2007
First available in Project Euclid: 2 October 2007

MathSciNet: MR2354916
Digital Object Identifier: 10.2178/jsl/1191333857

Rights: Copyright © 2007 Association for Symbolic Logic

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Vol.72 • No. 3 • September 2007
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