A type of mathematical result which is considered by most logicians as more natural than the metamathematical incompleteness results first discovered by Gödel. Finite combinatorial examples include Goodstein's theorem, a finite form of Ramsey's theorem, and a finite form of Kruskal's tree theorem (Kirby and Paris 1982; Smorynski 1980, 1982, 1983; Gallier 1991).

Gödel's first incompleteness theorem | Gödel's second incompleteness theorem | Goodstein's theorem | Kruskal's tree theorem | Ramsey's theorem