Fodor's Lemma, also called the pressing-down lemma, was proved by the Hungarian set theorist Geza Fodor in 1956. It states that if kappa is a regular uncountable cardinal, S is a stationary subset of kappa, and f is a regressive function on S, meaning f(alpha) is less than alpha for every nonzero alpha in S, then f is constant on some stationary subset of S. The lemma is equivalent to the statement that the nonstationary ideal on kappa is a normal ideal, and it is one of the basic tools used throughout set theory wherever stationary sets and cardinal arithmetic are studied.
Facts
StatementIf kappa is a regular uncountable cardinal, S is a stationary subset of kappa, and f from S to kappa is regressive (f(alpha) < alpha for every nonzero alpha in S), then there is some gamma and some stationary S0 contained in S such that f(alpha) = gamma for all alpha in S0. 1 Classification
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Source Fodor's lemma, Wikipedia
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1. Fodor's lemma, Wikipedia
Lead section
The lemma was first proved by the Hungarian set theorist, Géza Fodor in 1956.
Lead paragraph, history sentence
The lemma was first proved by the Hungarian set theorist, Géza Fodor in 1956.
In Branch: Set Theory, Lead sentence
In mathematics, particularly in set theory, Fodor's lemma (or the pressing-down lemma) states: In modern parlance, the nonstationa
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