A note on Σ 1 -maximal models

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Journal of Symbolic Logic 72 (3):1072-1078 (2007)
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Abstract

LetTbe a recursive theory in the language of first order Arithmetic. We prove that ifTextends: (a) the scheme of parameter free Δ1-minimization (plusexp). or (b) the scheme of parameter free Π1-induction, then there are no Σ1-maximal models with respect toT. As a consequence, we obtain a new proof of an unpublished theorem of Jeff Paris stating that Σ1-maximal models with respect toIΔ0+expdo not satisfy the scheme of Σ1-collectionBΣ1.

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10.2178/jsl/1191333857

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