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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].

MSC:

03E02 Partition relations

Citations:

Zbl 1197.03001
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