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
Statement Form Statement Form Connections
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Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
In Branch
Source Fodor's lemma, Wikipedia
Sources
1. Fodor's lemma, Wikipedia
Statement of the lemma
If κ is a regular, uncountable cardinal, S is a stationary subset of κ, and f : S → κ is regressive (that is, f(α) < α for any α ∈ S, α ≠ 0) then there is some γ and some stationary S₀ ⊆ S such that f(α) = γ for any α ∈ S₀.
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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