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.

Cofinality strata, trace, and reflection

Definition

For an ordinal $θ$ and an infinite regular cardinal $λ$ , write $E_{λ}^{θ} = {α < θ : cf (α) = λ}$ . For an ordinal $κ$ and $S \subseteq κ$ , define

$Tr (S) = {α < κ : cf (α) > ω and S \cap α is stationary in α} .$

We say $S$ reflects at $α$ when $α \in Tr (S)$ , and is nonreflecting when its trace is empty. Stationarity in $α$ uses clubs in that ordinal; it does not require $α$ to be a cardinal, but the trace definition restricts its cofinality to be uncountable.

Depends on

Used by

A trace computation for cofinality strata Example
Removing the trace preserves a stationary remainder Lemma
Splitting stationary sets of fixed smaller cofinality Lemma
Square and club-guessing orientation Remark
Regular cofinality strata are stationary Theorem

Dependency tree · two levels

9 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

Lietz, Definitions 5.12 and 5.15, pp.42–43 (standard reference, not scraped)
Vasey, Definition 15.6, p.85 (standard reference, not scraped)