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**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 < \omega_{1}, *Nosal* has several new results on \omega^{l} ––> (\omega^{n},m)^{2} and *Laver* proved several of our conjectures on ordered sets, and last but not least *Hajnal* proved \omega^{2}_{1} (not)––> (\omega^{2}_{1},3)^{2}. The later results of *Hajnal* and *Baumgartner* give a complete discussion of the truth value of \omega^{2}_{\alpha} ––> (\omega^{2}_{\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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