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Partition Theorems from Creatures and Idempotent Ultrafilters

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Abstract

We show a general scheme of Ramsey-type results for partitions of countable sets of finite functions, where “one piece is big” is interpreted in the language originating in creature forcing. The heart of our proofs follows Glazer’s proof of the Hindman Theorem, so we prove the existence of idempotent ultrafilters with respect to suitable operation. Then we deduce partition theorems related to creature forcings.

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Authors and Affiliations

  1. Department of Mathematics, University of Nebraska at Omaha, Omaha, NE, 68182-0243, USA

    Andrzej Rosłanowski

  2. Einstein Institute of Mathematics, Edmond J. Safra Campus, Givat Ram, The Hebrew University of Jerusalem, Jerusalem, 91904, Israel

    Saharon Shelah

  3. Department of Mathematics, Rutgers University, Hill Center - Busch Campus, 110 Frelinghuysen Road, Piscataway, NJ, 08854-8019, USA

    Saharon Shelah

Authors
  1. Andrzej Rosłanowski
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  2. Saharon Shelah
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Correspondence to Andrzej Rosłanowski.

Additional information

This research was supported by the United States-Israel Binational Science Foundation (Grant no. 2006108). Publication 957.

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Rosłanowski, A., Shelah, S. Partition Theorems from Creatures and Idempotent Ultrafilters. Ann. Comb. 17, 353–378 (2013). https://doi.org/10.1007/s00026-013-0184-7

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  • DOI: https://doi.org/10.1007/s00026-013-0184-7

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