Displaying similar documents to “A few Remarks on n-infinite Forcing Companions”

Strong initial segments of models of IΔ₀

Paola D'Aquino, Julia F. Knight (2007)

Fundamenta Mathematicae

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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...

A viewpoint on amalgamation classes

Silvia Barbina, Domenico Zambella (2010)

Commentationes Mathematicae Universitatis Carolinae

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We give a self-contained introduction to universal homogeneous models (also known as rich models) in a general context where the notion of morphism is taken as primitive. We produce an example of an amalgamation class where each connected component has a saturated rich model but the theory of the rich models is not model-complete.