Strong initial segments of models of IΔ₀

• Autorzy: Paola D'Aquino , Julia F. Knight
• Języki publikacji: EN

Abstrakty

EN

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 can be included.

Kategorie tematyczne

• 03H15: Nonstandard models of arithmetic
• 03C62: Models of arithmetic and set theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2007
• Tom: 195
• Numer: 2
• Strony: 155-176

Daty

wydano

2007

Twórcy

autor

Paola D'Aquino

• Dipartimento di Matematica, Seconda Università di Napoli, via Vivaldi 43, Caserta 81100, Italy

autor

Julia F. Knight

• Mathematics Department, University of Notre Dame, 255 Hurley Hall, Notre Dame, IN 46556, U.S.A.

Identyfikatory

DOI

10.4064/fm195-2-4