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An overview of a formalization project in the proof assistant Isabelle/HOL of a number of research results in infinitary combinatorics and set theory by Erdős–Milner, Specker, Larson and Nash-Williams, leading to Larson's proof of the unpublished result by E.C. Milner asserting that for all.
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Dedekind’s pigeon-hole principle, also known as the box argument or the chest of drawers argument (Schubfachprinzip) can be described, rather vaguely, as follows. If sufficiently many objects are…
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If S is an ordered set we write tp S to denote the order type of S and |5| for the cardinal of S. We also write [S] k for the set {X:X ⊂ S, |X|=k}. The partition symbol (1)
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In order to make (19) correct we define X., S(n) (n<(o) a little more caref lly and replace lines 21-31 on Page 504 by the following : Let n < co and s ppose that we have already chosen elements xi c…
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The theory provides two type classes with the aim of facilitating developments that combine V with other Isabelle/HOL types: embeddable, the class of types that can be injected into V (including V itself as well as V*V, V list, etc.), and small, theclasses that correspond to some ZF set.