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Diamond and antichains

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Abstract.

It is obvious that ♦ implies the existence of an antichain of stationary sets of cardinality which is the largest possible cardinality. We show that the obvious antichain is not maximal and find a less obvious extension of it by ℵ2 more stationary sets.

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Authors and Affiliations

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

    James Cummings & Ernest Schimmerling

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

Additional information

Mathematics Subject Classification (2000): 03E

The research of the authors is partially supported by the NSF.

The second author was partially supported by IHES during his June 5–25, 2002, visit. He thanks Stevo Todorcevic and Boban Velickovic for conversations during the visit on the main question answered in this report.

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Cummings, J., Schimmerling, E. Diamond and antichains. Arch. Math. Logic 44, 71–76 (2005). https://doi.org/10.1007/s00153-004-0247-x

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  • DOI: https://doi.org/10.1007/s00153-004-0247-x

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