Editing Decidability (logic) (section)

==In context of games==
Some [[games]] have been classified as to their decidability:
* Mate in ''n'' in [[infinite chess]] (with limitations on rules and gamepieces) is decidable.<ref name="Decidability">[https://mathoverflow.net/q/27967 Mathoverflow.net/Decidability-of-chess-on-an-infinite-board Decidability-of-chess-on-an-infinite-board]</ref><ref name="Mate in N">{{cite book |first1=Dan |last1=Brumleve |first2=Joel David |last2=Hamkins |first3=Philipp |last3=Schlicht |chapter=The Mate-in-n Problem of Infinite Chess Is Decidable |chapter-url=https://link.springer.com/chapter/10.1007%2F978-3-642-30870-3_9 |title=Conference on Computability in Europe |publisher=Springer |date=2012 |isbn=978-3-642-30870-3 |pages=78–88 |doi=10.1007/978-3-642-30870-3_9 |series=Lecture Notes in Computer Science |volume=7318 |arxiv=1201.5597|s2cid=8998263 }}</ref>  However, there are positions (with finitely many pieces) that are forced wins, but not mate in ''n'' for any finite ''n''.<ref>{{Cite web|url=https://mathoverflow.net/q/63423 |title=Lo.logic – Checkmate in $\omega$ moves?}}</ref>
* Some team games with imperfect information on a finite board (but with unlimited time) are undecidable.<ref>{{cite book |first=Bjorn |last=Poonen |chapter=10. Undecidable Problems: A Sampler: §14.1 Abstract Games |chapter-url=https://books.google.com/books?id=ulw3BAAAQBAJ&pg=PA211 |editor-first=Juliette |editor-last=Kennedy |title=Interpreting Gödel: Critical Essays |publisher=Cambridge University Press |date=2014 |isbn=9781107002661 |pages=211–241 See p. 239 |arxiv=1204.0299 |citeseerx=10.1.1.679.3322}}</ref>