DefinitionDefinition: Literature-sourcedProof: Not applicablePipeline-generatedjudge pass (gpt-5.6-terra)audited 2026-09-06

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.

Relative computability and relative enumerability

Definition

For an oracle $X \subseteq N$ , an oracle computation is an ordinary machine computation with a query instruction which receives the truthful bit for a queried number. A set $A$ is $X$ -computable when an $X$ -oracle machine decides it, and $X$ -c.e. when one recognizes it. Write $A \leq_{T} X$ for $X$ -computability, consistently with Turing reductions via oracle deciders.

An oracle program still makes finitely many transitions on any halting run; it does not read an infinite oracle at once.

Used by

A diagonal set at each arithmetical level Lemma
An oracle computation has a finite query witness Lemma
Post's theorem Theorem
Shoenfield's limit lemma Theorem

Dependency tree · 0 levels

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

Sources

Ludovic Patey, Computability Theory, §4.2 (standard reference, not scraped)