Zentralblatt MATH

Publications of (and about) Paul Erdös

Zbl.No:  559.04009
Autor:  Baumgartner, James E.; Erdös, Paul; Higgs, D.
Title:  Cross-cuts in the power set of an infinite set. (In English)
Source:  Order 1, 139-145 (1984).
Review:  Authors' 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\subseteq E satisfy X\subseteq Y, X\subseteq some X' in C, and Y\supseteq some Y' in C, then X\subseteq Z\subseteq Y for some Z in C. For E = \omega, \omega1 and \omega2, it is shown with the aid of the continuum hypothesis that P(E) has cross-cuts consisting of infinite sets with infinite complements, and somewhat stronger results are proved for \omega and \omega1.''
Reviewer:  N.H.Williams
Classif.:  * 04A20 Combinatorial set theory
                   06A06 Partial order
                   04A30 Continuum hypothesis and generalizations
Keywords:  power set; sets of a fixed finite cardinality; cross-cut; maximal unordered set; continuum hypothesis

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