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.
FALSE: the Novikov-Boone theorem proves only the uniform problem is unsolvable
Statement
Assume the Axiom of Choice. The Novikov-Boone theorem shows at most that the uniform word problem for finite presentations is unsolvable.
Facts & Assumptions
Given: The Axiom of Choice (The Axiom of Choice) and the Novikov-Boone theorem.
Under the given Choice premise, the Novikov-Boone theorem supplies one fixed finite presentation with unsolvable word problem. (Novikov boone undecidability of the word problem)
Refutation
By [L1], Novikov-Boone already produces one fixed finitely presented group whose word problem is unsolvable.
A theorem about one fixed finitely presented group is stronger than a statement that only the varying-presentation problem fails. So the theorem is not limited to the uniform problem.
Therefore the statement is false.
Depends on
Used by
Nothing in the library uses this result yet.
Dependency tree · two levels
9 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
- Charles F. Miller III, Decision Problems for Groups - Survey and Reflections (standard reference, not scraped)