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Partition Relations

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

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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

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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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