Kanamori–McAloon theorem

Kanamori–McAloon theorem In mathematical logic, the Kanamori–McAloon theorem, due to Kanamori & McAloon (1987), gives an example of an incompleteness in Peano arithmetic, similar to that of the Paris–Harrington theorem. They showed that a certain finitistic theorem in Ramsey theory is not provable in Peano arithmetic (Pennsylvanie).

Statement Given a set {displaystyle ssubseteq mathbb {N} } of non-negative integers, laisser {displaystyle min(s)} denote the minimum element of {style d'affichage s} . Laisser {style d'affichage [X]^{n}} denote the set of all n-element subsets of {style d'affichage X} .

A function {style d'affichage f:[X]^{n}flèche droite mathbb {N} } où {displaystyle Xsubseteq mathbb {N} } is said to be regressive if {style d'affichage f(s)

Si vous voulez connaître d'autres articles similaires à Kanamori–McAloon theorem vous pouvez visiter la catégorie Independence results.