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.
Adian-Rabin: every Markov property is undecidable on finite presentations
Statement
Every Markov property of finitely presented groups is undecidable on finite presentations.
Remarks
The witness groups required by A Markov property of finitely presented groups are part of the theorem's hypotheses, not a dispensable ornament. The point is that a positive witness and an obstruction witness let one encode arbitrary word-problem instances into finite presentations whose possession of the property detects the original instance.
This page records that reduction as a boundary theorem only. It does not rebuild the Adian-Rabin construction.
Depends on
Used by
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
- Alex Bishop, Minicourse: On Decision Problems in Groups (standard reference, not scraped)
- MacTutor History of Mathematics, Word problems (standard reference, not scraped)