Geodesic
Strong initial segments of models of $I\Delta_0$
Paola D'Aquino 1   ; Julia F. Knight 2
1 Dipartimento di Matematica Seconda Università di Napoli via Vivaldi 43 Caserta 81100, Italy
2 Mathematics Department University of Notre Dame 255 Hurley Hall Notre Dame, IN 46556, U.S.A.
Fundamenta Mathematicae, Tome 195 (2007) no. 2, pp. 155-176 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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McAloon showed that if ${\cal A}$ is a nonstandard model of $I\Delta_0$, then some initial segment of ${\cal A}$ 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 ${\cal A}$ of $I\Delta_0$ 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.
DOI : 10.4064/fm195-2-4
Keywords: mcaloon showed cal nonstandard model delta initial segment cal nonstandard model sommer daquino characterized terms wainer functions elements belong initial segment characterization work ketonen solovay paris here conditions model cal delta guaranteeing there n elementary initial segment nonstandard model characterize elements included

Paola D'Aquino  1   ; Julia F. Knight  2

1 Dipartimento di Matematica Seconda Università di Napoli via Vivaldi 43 Caserta 81100, Italy
2 Mathematics Department University of Notre Dame 255 Hurley Hall Notre Dame, IN 46556, U.S.A. 
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Paola D'Aquino; Julia F. Knight. Strong initial segments of models of $I\Delta_0$. Fundamenta Mathematicae, Tome 195 (2007) no. 2, pp. 155-176. doi: 10.4064/fm195-2-4

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