Journal of Symbolic Logic

A note on Σ1-maximal models

A. Cordón—Franco and F. F. Lara—Martín

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Π1-induction, then there are no Σ1-maximal models with respect to T. As a consequence, we obtain a new proof of an unpublished theorem of Jeff Paris stating that Σ1-maximal models with respect to IΔ0 + exp do not satisfy the scheme of Σ1-collection BΣ1.

Article information

Source
J. Symbolic Logic, Volume 72, Issue 3 (2007), 1072-1078.

Dates
First available in Project Euclid: 2 October 2007

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1191333857

Digital Object Identifier
doi:10.2178/jsl/1191333857

Mathematical Reviews number (MathSciNet)
MR2354916

Citation

Cordón—Franco, A.; Lara—Martín, F. F. A note on Σ 1 -maximal models. J. Symbolic Logic 72 (2007), no. 3, 1072--1078. doi:10.2178/jsl/1191333857. https://projecteuclid.org/euclid.jsl/1191333857


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