The minimal e-degree problem in fragments of Peano arithmetic
نویسندگان
چکیده
We study the minimal enumeration degree (e-degree) problem in models of fragments of Peano arithmetic (PA) and prove the following results: In any model M of Σ2 induction, there is a minimal enumeration degree if and only if M is a nonstandard model. Furthermore, any cut in such a model has minimal e-degree. By contrast, this phenomenon fails in the absence of Σ2 induction. In fact, whether every Σ2 cut has minimal e-degree is independent of the Σ2 bounding principle.
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ورودعنوان ژورنال:
- Ann. Pure Appl. Logic
دوره 131 شماره
صفحات -
تاریخ انتشار 2005