DefinitionDefinition: Literature-sourcedProof: Not applicablePipeline-generatedjudge pass (gpt-5.6-terra)audited 2026-09-07

How statement and proof provenance work

The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.

Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.

These labels describe origin, not correctness: citations and verification chips remain separate evidence.

Regressive functions on ordinals

Definition

For $S \subseteq κ ∖ {0}$ , a map $f : S \to κ$ is regressive if $f (α) < α$ for every $α \in S$ . If an original domain contains zero, regression is asserted only after explicitly restricting to its complement: no ordinal is less than zero.

Used by

An unbounded regressive domain without a stationary fibre Counterexample
Fodor’s pressing-down lemma Theorem
Normality is equivalent to positive pressing down Theorem

Dependency tree · 0 levels

Nothing. This result depends on no other item in the library.

Sources

Lietz, Definition 5.10, p.41 (standard reference, not scraped)
Vasey, Definition 15.1, p.82 (standard reference, not scraped)