Acta Mathematica Hungarica

, Volume 154, Issue 1, pp 231–242 | Cite as

Fodor’s lemma can fail everywhere

  • A. KaragilaEmail author


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.

Key words and phrases

symmetric extension Fodor’s lemma closed and unbounded filter iterated symmetric extension the axiom of choice 

Mathematics Subject Classification

primary 03E40 secondary 03E05 03E25 03E35 


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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2017

Authors and Affiliations

  1. 1.Einstein Institute of Mathematics, Edmond J. Safra Campus, Givat RamThe Hebrew University of JerusalemJerusalemIsrael
  2. 2.DMG/AlgebraTU WienWienAustria

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