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.

Turing reducibility and equivalence

Definition

For sets $A, B \subseteq N$ , write $A \leq_{T} B$ when one oracle machine $M$ decides $A$ with oracle $B$ : for every $n$ , $M^{B} (n) ↓$ and its output is $1$ iff $n \in A$ . Write $A \equiv_{T} B$ when both $A \leq_{T} B$ and $B \leq_{T} A$ ; this is Turing equivalence.

Depends on

Oracle Turing machines

Used by

Computably dominated oracles Definition
Turing degrees and their order Definition
The jump is well-defined on degrees Lemma
Turing reducibility is a preorder Lemma
Truth-table reducibility implies Turing reducibility Proposition
Computable domination characterizes truth-table reducibility Theorem
The jump is monotone 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

Sebastiaan Terwijn, Computability Theory, Definition 5.1.3 (standard reference, not scraped)