A model of second-order arithmetic satisfying AC but not DC
Logic
2018-08-16 v2
Abstract
We show that there is a -model of second-order arithmetic in which the choice scheme holds, but the dependent choice scheme fails for a -assertion, confirming a conjecture of Stephen Simpson. We obtain as a corollary that the Reflection Principle, stating that every formula reflects to a transitive set, can fail in models of . This work is a rediscovery by the first two authors of a result obtained by the third author.
Keywords
Cite
@article{arxiv.1808.04732,
title = {A model of second-order arithmetic satisfying AC but not DC},
author = {Sy-David Friedman and Victoria Gitman and Vladimir Kanovei},
journal= {arXiv preprint arXiv:1808.04732},
year = {2018}
}