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.

Normal ordinal functions

Definition

For a regular uncountable cardinal $κ$ , a function $f : κ \to κ$ is normal if it is strictly increasing and, for each nonzero limit $λ < κ$ ,

$f (λ) = \sup_{ξ < λ} f (ξ) .$

There is no requirement that $f (0) = 0$ . The analogous notation for a class function on all ordinals uses the same two clauses, but the theorems on this page have the set domain $κ$ .

Depends on

Closed unbounded subsets of ordinals

Used by

Square and club-guessing orientation Remark
Clubs are ranges of normal enumerations Theorem
Fixed points of a normal function form a club Theorem

Dependency tree · two levels

2 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.

Sources

Vasey, Definition 14.3, p.80 (standard reference, not scraped)
Welch, Definition 2.11, printed p.20; live original reread (standard reference, not scraped)