Completion closed algebras and models of Peano arithmetic

Petr Hájek

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Fragments of complete extensions of PA and McDowell-Specker's theorem.

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Strong initial segments of models of IΔ₀

Paola D&#039;Aquino, Julia F. Knight (2007)

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McAloon showed that if 𝓐 is a nonstandard model of IΔ₀, then some initial segment of 𝓐 is a nonstandard model of PA. Sommer and D'Aquino characterized, in terms of the Wainer functions, the elements that can belong to such an initial segment. The characterization used work of Ketonen and Solovay, and Paris. Here we give conditions on a model 𝓐 of IΔ₀ guaranteeing that there is an n-elementary initial segment that is a nonstandard model of PA. We also characterize the elements that...