Alphabeta MathHow 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.
Shoenfield orientation and hierarchy conventions
Remarks
The projective hierarchy quantifies over reals with arithmetic matrices. The set-theoretic Lévy hierarchy quantifies over sets with bounded membership matrices. A mention of Shoenfield absoluteness is therefore not an application of this page's upward theorem.
Compare The Lévy hierarchy and absoluteness and Sigma-one truth goes upward. Kamensky, §5.2, pp.45–47, explains the distinct real-coding problem; its printed Shoenfield sketch omits a coding argument. Additional descriptive-set-theoretic coding and absoluteness machinery is required before that result could be a supplier. No Shoenfield theorem is asserted or used here.
Depends on
Used by
Nothing in the library uses this result yet.
Dependency tree · two levels
6 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.