English

Remark on the Failure of Martin's Axiom

Logic 2008-02-03 v1

Abstract

Let m be the least cardinal k such that MA(k) fails. The only known model for "m is singular" was constructed by Kunen. In Kunen's model cof(m)=omega_1. It is unknown whether "omega_1 < cof(m) < m" is consistent. The purpose of this paper is to present a proof of Kunen's result and to identify the difficulties of generalizing this result to an arbitrary uncountable cofinality.

Keywords

Cite

@article{arxiv.math/9207205,
  title  = {Remark on the Failure of Martin's Axiom},
  author = {Avner Landver},
  journal= {arXiv preprint arXiv:math/9207205},
  year   = {2008}
}