Fodor's lemma can fail everywhere
classification
🧮 math.LO
keywords
everywherefodorlemmacardinalclubcompletecontrolledequiconsistent
read the original 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.
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