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Partition Relations

In: Handbook of Set Theory

Author

Listed:
  • András Hajnal

    (Hungarian Academy of Sciences, Alfred Renyi Institute of Mathematics)

  • Jean A. Larson

    (University of Florida, Department of Mathematics)

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.

Suggested Citation

  • András Hajnal & Jean A. Larson, 2010. "Partition Relations," Springer Books, in: Matthew Foreman & Akihiro Kanamori (ed.), Handbook of Set Theory, chapter 2, pages 129-213, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4020-5764-9_3
    DOI: 10.1007/978-1-4020-5764-9_3
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