The minimal e-degree problem in fragments of Peano arithmetic

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 2 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 2 induction. In fact, whether every 2 cut has minimal e-degree is independent of the 2 bounding principle.

• Type: Journal
• Year: 2005
• Where: APAL
• Authors: Marat M. Arslanov, Chi Tat Chong, S. Barry Cooper, Yue Yang
• Keywords: APAL 2005, Minimal E-degree, Minimal Enumeration Degree, Model