Cofinal Extensions and Coded Sets
Logic
2017-08-04 v1
Abstract
Let M be a model of Peano Arithmetic that is countably generated over an exponentially closed cut I. We characterize those sets X of subsets of I for which there is a finitely (or countably) generated cofinal extension N of M such that I is the Greatest Common Initial Segment of M and N and X is the set of subsets of I coded by the extension. We also characterize such X for which the extension N can be, in addition, one of the following: non-filling; filling; n-filling.
Keywords
Cite
@article{arxiv.1708.00899,
title = {Cofinal Extensions and Coded Sets},
author = {James H. Schmerl},
journal= {arXiv preprint arXiv:1708.00899},
year = {2017}
}