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: every finitely presented group has solvable word problem
Statement
Assume the Axiom of Choice (The Axiom of Choice). Every finitely presented group has solvable word problem.
Facts & Assumptions
Given: The Axiom of Choice and the local Novikov-Boone existence theorem.
Under AC, one fixed finitely presented group has an unsolvable word problem (Novikov boone undecidability of the word problem).
Refutation
By [L1], there exists a finitely presented group whose word problem is unsolvable.
That group is a counterexample to the statement, so 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)