Fodor's lemma: Difference between revisions
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(Created page with "'''Fodor's lemma''' (or the '''pressing-down lemma''') is a lemma proven by Géza Fodor in 1956. The lemma states that when \(\kappa\) is an uncountable regular cardinal and \(S\) is a stationary set of ordinals \(<\kappa\), any regressive function \(f:S\to\{<\kappa\}\) must be constant on a stationary set of ordinals \(<\kappa\). ==Importance to apierology== Since \(\omega_1\) is regular, setting \(S=\{<\omega_1\}\), Fodor's lemma implies there does not exist a fundame...") |
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==Importance to apierology==
Since \(\omega_1\) is regular, setting \(S=\{<\omega_1\}\), Fodor's lemma implies there does not exist a fundamental sequence system that both assigns a sequence to all countable ordinals, and has the Bachmann property. Fodor's lemma may fail without choice<nowiki><ref>A. Karagila, </nowiki>[https://arxiv.org/abs/1610.03985 Fodor's Lemma can Fail Everywhere]<nowiki></ref></
==References==
* E. Tachtsis, [https://www.ams.org/journals/proc/2020-148-03/S0002-9939-2019-14794-8/S0002-9939-2019-14794-8.pdf Juhász's topological generalization of Neumer's theorem may fail in ZF] (2019). Corollary 2.7.
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