KnowraGoodstein's theoremLinked fromLinked fromThe 6 pages that link to Goodstein's theorem, each with the reason it gives.All 6Broader topic 2Related 2Compared with 2Peano arithmeticRelated: Its truth is provable in stronger systems but not in Peano arithmetic.Independence (mathematical logic)Broader topic: It illustrates independence from a particular arithmetic system without being independent of ordinary mathematics.Transfinite inductionRelated: Its standard proof maps sequence steps to descending ordinals and rules out infinite descent.Paris–Harrington theoremCompared with: Like Paris–Harrington, it is true but unprovable in Peano arithmetic.Gödel's first incompleteness theoremBroader topic: Kirby and Paris showed in 1982 it is a natural sentence independent of Peano arithmetic.Kruskal's tree theoremCompared with: Like Kruskal's theorem, it is true but not provable in Peano arithmetic.