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An ℵ1-dense ideal on ℵ2

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Abstract

This paper establishes the consistency of a countably complete, uniform, ℵ1-dense ideal on ℵ2. As a corollary, it is consistent that there exists a uniform ultrafilterD on ω2 such that |ω ω21 D|=ω1. A general “transfer” result establishes the consistency of countably complete uniform ideal K on ω2 such thatP(ω2)/K≅P(ω1)/ {countable sets}.

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Authors and Affiliations

  1. Department of Mathematics, University of California at Irvine, 92697-3857, Irvine, CA, USA

    Matthew Foreman

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  1. Matthew Foreman
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Correspondence to Matthew Foreman.

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Partially supported by an NSF grant.

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Foreman, M. An ℵ1-dense ideal on ℵ2 . Israel J. Math. 108, 253–290 (1998). https://doi.org/10.1007/BF02783051

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  • DOI: https://doi.org/10.1007/BF02783051

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