Fodor's lemma: Difference between revisions
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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
==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.
* Karel Hrbacek & Thomas Jech, Introduction to Set Theory, 3rd edition, Chapter 11, Section 3.
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