Zentralblatt MATH

Publications of (and about) Paul Erdös

Zbl.No:  251.04004
Autor:  Erdös, Paul
Title:  Problems in combinatorial set theory. (In English)
Source:  Combinat. Struct. Appl., Proc. Calgary internat. Conf. combinat. Struct. Appl., Calgary 1969, 97-100 (1970).
Review:  [For the entire collection see Zbl 243.00004.]
Several solved and unsolved problems on partition calculus are discussed. Here I only state those problems which are mentioned in the paper and which have been solved since then. Jean Larson and Eric Milner proved \omega\omega ––> (\omega\omega,n)2, Baumgartner and Hajnal proved \lambda ––> (\alpha,..., \alpha)2 for every \alpha < \omega1, Nosal has several new results on \omegal ––> (\omegan,m)2 and Laver proved several of our conjectures on ordered sets, and last but not least Hajnal proved \omega21 (not)––> (\omega21,3)2. The later results of Hajnal and Baumgartner give a complete discussion of the truth value of \omega2\alpha ––> (\omega2\alpha,3)2.
Classif.:  * 04A10 Ordinal and cardinal numbers; generalizations
05A17 Partitions of integres (combinatorics)
05-02 Research monographs (combinatorics)
04A20 Combinatorial set theory
00A07 Problem books

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