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Archive for Mathematical Logic

, Volume 55, Issue 7–8, pp 857–865 | Cite as

Mathias forcing and ultrafilters

  • Janusz Pawlikowski
  • Wojciech Stadnicki
Open Access
Article
  • 203 Downloads

Abstract

We prove that if the Mathias forcing is followed by a forcing with the Laver Property, then any \(\mathsf {V}\)-\(\mathsf {q}\)-point is isomorphic via a ground model bijection to the canonical \(\mathsf {V}\)-Ramsey ultrafilter added by the Mathias real. This improves a result of Shelah and Spinas (Trans AMS 325:2023–2047, 1999).

Keywords

Mathias forcing Ramsey ultrafilter Laver property 

References

  1. 1.
    Blass, A.: MR1751223 (2001f:03095), Mathematical ReviewsGoogle Scholar
  2. 2.
    Shelah, S., Spinas, O.: The distributivity numbers of \({\cal P} (\omega )/{{\rm fin}}\) and its square. Trans. AMS 325, 2023–2047 (1999)MathSciNetzbMATHGoogle Scholar

Copyright information

© The Author(s) 2016

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of WrocławWrocławPoland

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