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.

Local GCH for arbitrary sets

Definition

Write $X ⪯ Y$ for an injection and $X \approx Y$ for a bijection; $X ≺ Y$ means $X ⪯ Y$ and $X \approx̸ Y$ . For an infinite set $X$ , local GCH at $X$ , denoted $C H (X)$ , means

$\forall Y (X ⪯ Y ⪯ P (X) ⟹ Y \approx X or Y \approx P (X)) .$

Arbitrary-set GCH asserts this for every infinite set. No well-order of $X$ is implicit. We write $Seq (X) = ⋃_{n < ω}^{n} X$ for finite sequences, including the empty sequence, and $h (X)$ for the Hartogs number. Disjoint union is denoted $⊔$ .

Local GCH for arbitrary sets

Definition

Depends on

Dependency tree · 2 levels

Sources