Hajnal, András; Larson, Jean A. Partition relations. (English) Zbl 1198.03048 Foreman, Matthew (ed.) et al., Handbook of set theory. In 3 volumes. Dordrecht: Springer (ISBN 978-1-4020-4843-2/hbk; 978-1-4020-5764-9/ebook). 129-213 (2010). Summary: Partition relations were introduced in 1952 by Paul Erdős and Richard Rado to generalize Ramsey’s Theorem, yielding a seemingly inexhaustible supply of interesting problems. Unlike other classical problems these are far from being completely solved; indeed, there are only a few new deep results. We showcase modern methods of combinatorial set theory by giving new complete proofs of some of these deep results in a unified framework of nonreflecting ideals, using elementary submodels. In the last section we give a separate overview of the recent deep developments for countable underlying sets.See also the review of the complete volume [Zbl 1197.03001].For the entire collection see [Zbl 1197.03001]. Cited in 15 Documents MSC: 03E02 Partition relations Citations:Zbl 1197.03001 PDFBibTeX XMLCite \textit{A. Hajnal} and \textit{J. A. Larson}, in: Handbook of set theory. In 3 volumes. Dordrecht: Springer. 129--213 (2010; Zbl 1198.03048) Full Text: DOI