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 (PA).

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

A function {displaystyle f:[X]^{n}rightarrow mathbb {N} } where {displaystyle Xsubseteq mathbb {N} } is said to be regressive if {displaystyle f(s)

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