The minimal e-degree problem in fragments of Peano arithmetic

Annals of Pure and Applied Logic 131 (1-3):159-175 (2005)
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Abstract

We study the minimal enumeration degree problem in models of fragments of Peano arithmetic () 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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Yingluo Yang
Renmin University of China

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References found in this work

Partial degrees and the density problem.S. B. Cooper - 1982 - Journal of Symbolic Logic 47 (4):854-859.
The degree of a Σn cut.C. T. Chong & K. J. Mourad - 1990 - Annals of Pure and Applied Logic 48 (3):227-235.

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