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Partition Relations

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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.

Research partially supported by NSF grants DMS-0072560 (Hajnal) and DMS-9970536 (Larson), and by grant HNFSR-68262 (Hajnal).

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Authors and Affiliations

  1. Alfred Renyi Institute of Mathematics, Hungarian Academy of Sciences, Budapest, Hungary

    András Hajnal

  2. Department of Mathematics, University of Florida, Gainsville, FL, 32611, USA

    Jean A. Larson

Authors
  1. András Hajnal
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  2. Jean A. Larson
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Correspondence to András Hajnal .

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Editors and Affiliations

  1. School of Physical Sciences, University of California, Irvine, Irvine, 92697-3875, U.S.A.

    Matthew Foreman

  2. Dept. Manufacturing Engineering, Boston University, St. Mary's St. 15, Boston, 02215, U.S.A.

    Akihiro Kanamori

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Hajnal, A., Larson, J.A. (2010). Partition Relations. In: Foreman, M., Kanamori, A. (eds) Handbook of Set Theory. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-5764-9_3

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