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|Title:||The minimal e-degree problem in fragments of Peano arithmetic|
|Citation:||Arslanov, M.M., Chong, C.T., Cooper, S.B., Yang, Y. (2005-01). The minimal e-degree problem in fragments of Peano arithmetic. Annals of Pure and Applied Logic 131 (1-3) : 159-175. ScholarBank@NUS Repository. https://doi.org/10.1016/j.apal.2004.04.010|
|Abstract:||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. © 2004 Elsevier B.V. All rights reserved.|
|Source Title:||Annals of Pure and Applied Logic|
|Appears in Collections:||Staff Publications|
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