The length of an intersection

Mathematical Logic Quarterly 63 (3-4):243-255 (2017)

Abstract

A poset math formula is well-partially ordered if all its linear extensions are well orders; the supremum of ordered types of these linear extensions is the length, math formula of p. We prove that if the vertex set X is infinite, of cardinality κ, and the ordering ⩽ is the intersection of finitely many well partial orderings math formula of X, math formula, then, letting math formula, with math formula, denote the euclidian division by κ of the length of each corresponding poset: math formula where math formula denotes the least initial ordinal greater than the ordinal math formula. This inequality is optimal. This result answers questions of Forster.

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