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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