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Gently killing S-spaces

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Abstract

We produce a model of ZFC in which there are no locally compact first countable S-spaces, and in which 2ℵ 0<2ℵ 1. A consequence of this is that in this model there are no locally compact, separable, hereditarily normal spaces of size ℵ1, answering a question of the second author [9].

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Northern Iowa, 50613, Cedar Falls, IA, USA

    Todd Eisworth

  2. Department of Mathematics, University of South Carolina, 29208, Columbia, SC, USA

    Peter Nyikos

  3. Institute of Mathematics, The Hebrew University of Jerusalem, 91904, Jerusalem, Israel

    Saharon Shelah

  4. Department of Mathematics, Rutgers University, 08903, New Brunswick, NJ, USA

    Saharon Shelah

Authors
  1. Todd Eisworth
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  2. Peter Nyikos
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  3. Saharon Shelah
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Corresponding author

Correspondence to Todd Eisworth.

Additional information

The first author would like to thank The Hebrew University of Jerusalem for their support while the research in this paper was being carried out.

The research of the second author was partially supported by NSF Grant DMS-9322613.

The research of the third author was partially supported by NSF grant DMS-9704477 and the Israel Science Foundation founded by the Israel Academy of Sciences and Humanities. This is publication number 690 in the list of the third author.

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Eisworth, T., Nyikos, P. & Shelah, S. Gently killing S-spaces. Isr. J. Math. 136, 189–220 (2003). https://doi.org/10.1007/BF02807198

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  • DOI: https://doi.org/10.1007/BF02807198

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