The minimal e-degree problem in fragments of Peano arithmetic

Please use this identifier to cite or link to this item: https://doi.org/10.1016/j.apal.2004.04.010

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
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
URI:	http://scholarbank.nus.edu.sg/handle/10635/104316
ISSN:	01680072
DOI:	10.1016/j.apal.2004.04.010
Appears in Collections:	Staff Publications

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