Partition Relations

András Hajnal () and Jean A. Larson ()
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András Hajnal: Hungarian Academy of Sciences, Alfred Renyi Institute of Mathematics
Jean A. Larson: University of Florida, Department of Mathematics

Chapter 2 in Handbook of Set Theory, 2010, pp 129-213 from Springer

Abstract: Abstract 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.

Keywords: Initial Segment; Order Type; Winning Strategy; Decision Node; Node Label (search for similar items in EconPapers)
Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4020-5764-9_3

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DOI: 10.1007/978-1-4020-5764-9_3

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