Cross-Cuts in the Power Set of an Infinite Set*

Abstract

In the power set P(E) of a set E, the sets of a fixed finite cardinality k form a cross-cut, that is, a maximal unordered set C such that if X, Y C E satisfy X c Y, X c some X' in C. and y : some Y' in C, then X C Z C Y for some Z in C. For E .= w, w, , and w, , it is shown with the aid of the continuum hypothesis that P(E) has cross-cuts consisting of… (More)

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