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).
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Blass, A.: MR1751223 (2001f:03095), Mathematical Reviews
Shelah, S., Spinas, O.: The distributivity numbers of \({\cal P} (\omega )/{{\rm fin}}\) and its square. Trans. AMS 325, 2023–2047 (1999)
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Partially supported by IM UWr Grant 2155/M/IM/14.
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Pawlikowski, J., Stadnicki, W. Mathias forcing and ultrafilters. Arch. Math. Logic 55, 857–865 (2016). https://doi.org/10.1007/s00153-016-0499-2
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DOI: https://doi.org/10.1007/s00153-016-0499-2