Fodor's lemma can fail everywhere

Abstract

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

Rev 3: Minor improvements. 10 pages

References in corpus (1)

• Embedding Orders Into Cardinals With $D{C}_{\kappa }$

Cited by in corpus (2)

• Galvin's property at large cardinals and an application to partition calculus
• The Morris model