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).

of non-negative integers, let

denote the minimum element of

denote the set of all n-element subsets of

The Kanamori–McAloon theorem states that the following proposition, denoted by

in the original reference, is not provable in PA:

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