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.
Two choice-theoretic questions beyond the local Hahn-Banach proof
Remark
The proof cost of the local Hahn-Banach theorem is summarized in The set-theoretic cost of Hahn-Banach. It is natural to ask what the extension principle alone, assumed over ZF, would imply:
- Does it imply that has a Hamel basis over ?
- Does it imply that there is a discontinuous additive map ?
These are questions, without an assertion of their current research status or an answer. Neither implication is a premise of the local extension proof.
Depends on
Used by
Nothing in the library uses this result yet.
Dependency tree · two levels
4 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
- P. Howard and J. E. Rubin, Consequences of the Axiom of Choice (standard reference, not scraped)
- P. Larson and S. Shelah, Discontinuous homomorphisms without Hamel bases (standard reference, not scraped)