Strong initial segments of models of $I\Delta_0$

Volume 195 / 2007

Paola D'Aquino, Julia F. Knight Fundamenta Mathematicae 195 (2007), 155-176 MSC: 03H15, 03C62. DOI: 10.4064/fm195-2-4


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.


  • Paola D'AquinoDipartimento di Matematica
    Seconda Università di Napoli
    via Vivaldi 43
    Caserta 81100, Italy
  • Julia F. KnightMathematics Department
    University of Notre Dame
    255 Hurley Hall
    Notre Dame, IN 46556, U.S.A.

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