Archive for Mathematical Logic

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

Mathias forcing and ultrafilters

  • Janusz Pawlikowski
  • Wojciech Stadnicki
Open Access


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).


Mathias forcing Ramsey ultrafilter Laver property 


  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 (, 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

Personalised recommendations