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

Let T be a recursive theory in the language of first order Arithmetic. We prove that if T extends: the scheme of parameter free Δ1-minimization, or 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free Π1-induction, then there are no Σ1-maximal models with respect to T. As a consequence, we obtain a new proof of an unpublished theorem of Jeff Paris stating that Σ1-maximal models with respect to IΔ0 + exp do not satisfy the scheme of Σ1-collection BΣ1.
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DOI 10.2178/jsl/1191333857
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