Separating the Fan Theorem and Its Weakenings
Logic
2015-10-09 v1
Abstract
Varieties of the Fan Theorem have recently been developed in reverse constructive mathematics, corresponding to different continuity principles. They form a natural implicational hierarchy. Some of the implications have been shown to be strict, others strict in a weak context, and yet others not at all, using disparate techniques. Here we present a family of related Kripke models which separates all of the as yet identified fan theorems.
Cite
@article{arxiv.1510.02141,
title = {Separating the Fan Theorem and Its Weakenings},
author = {Robert S. Lubarsky and Hannes Diener},
journal= {arXiv preprint arXiv:1510.02141},
year = {2015}
}