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Indexed squares

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Abstract

We study some combinatorial principles intermediate between square and weak square. We construct models which distinguish various square principles, and show that a strengthened form of weak square holds in the Prikry model. Jensen proved that a large cardinal property slightly stronger than 1-extendibility is incompatible with square; we prove this is close to optimal by showing that 1-extendibility is compatible with square.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Carnegie Mellon University, 15213-3890, Pittsburgh, PA, USA

    James Cummings & Ernest Schimmerling

Authors
  1. James Cummings
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  2. Ernest Schimmerling
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Correspondence to James Cummings.

Additional information

First author partially supported by NSF grants DMS-9703945 and DMS-0070549.

Second author partially supported by NSF Grants DMS-9305990, DMS-9712580, DMS-9996280 and DMS-0088948.

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Cummings, J., Schimmerling, E. Indexed squares. Isr. J. Math. 131, 61–99 (2002). https://doi.org/10.1007/BF02785851

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  • DOI: https://doi.org/10.1007/BF02785851

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