English

Fodor's lemma can fail everywhere

Logic 2018-05-15 v3

Abstract

We show that it is equiconsistent with ZF\mathsf{ZF} that Fodor's lemma fails everywhere, and furthermore that the club filter on every regular cardinal is not even σ\sigma-complete. Moreover, these failures can be controlled in a very precise manner.

Cite

@article{arxiv.1610.03985,
  title  = {Fodor's lemma can fail everywhere},
  author = {Asaf Karagila},
  journal= {arXiv preprint arXiv:1610.03985},
  year   = {2018}
}

Comments

Rev 3: Minor improvements. 10 pages

R2 v1 2026-06-22T16:19:33.097Z