Zentralblatt MATH
Publications of (and about) Paul Erdös
Zbl.No: 212.02204
Autor: Erdös, Paul; Milner, E.C.; Rado, R.
Title: Partition relations for \eta\alpha-sets (In English)
Source: J. Lond. Math. Soc., II. Ser. 3, 193-204 (1971).
Review: In terms of the partition symbol [see P. Erdös, A. Hajnal and R. Rado, Acta math. Acad. Sci. Hungar. 16, 93-196 (1965; Zbl 158.26603)] the main result proved in this paper is that if \aleph\alpha is regular, \aleph\alpha > \aleph\beta and GCH holds, then \eta\alpha ––> (\eta\alpha , \aleph\beta)2. It is not known whether the relations \eta\omega ––> (\eta\omega , \aleph0)2, \eta\omega ––> (\eta\omega ,3)2 hold. For the partitioning of triplets it is shown that, for any order type \phi, \phi \mapsto (\omega+\omega^*,4)3, \phi \mapsto (\omega^*+\omega,4), \phi \mapsto (\omega+\omega^* or \omega^*+\omega,5)3. It remains an open question whether this last relation holds with 4 in place of 5.
Classif.: * 04A20 Combinatorial set theory
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