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Title: The minimal e-degree problem in fragments of Peano arithmetic
Authors: Arslanov, M.M.
Chong, C.T. 
Cooper, S.B.
Yang, Y. 
Issue Date: Jan-2005
Source: 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.
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
ISSN: 01680072
DOI: 10.1016/j.apal.2004.04.010
Appears in Collections:Staff Publications

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