Prikry Forcings, Unger’s Lectures
نویسندگان
چکیده
منابع مشابه
Prikry Forcing with Long Extenders
In this note, we go through Gitik’s Long Extender forcing. In order to motivate it, work through the basic Pirkry forcing as well as the diagonal Prikry forcing. The presentation here is based on Spencer Unger’s lectures from the 2015 GSST in addition to Gitik’s Handbook chapter.
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We study the Mathias–Prikry and the Laver type forcings associated with filters and coideals. We isolate a crucial combinatorial property of Mathias reals, and prove that Mathias–Prikry forcings with summable ideals are all mutually bi-embeddable. We show that Mathias forcing associated with the complement of an analytic ideal does add a dominating real. We also characterize filters for which t...
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We study the Mathias-Prikry and Laver-Prikry forcings associated with filters on ω. We give a combinatorial characterization of Martin’s number for these forcing notions and present a general scheme for analyzing preservation properties for them. In particular, we give a combinatorial characterization of those filters for which the Mathias-Prikry forcing does not add any dominating reals.
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In order to present this result, we approach it by proving some preliminary theorems about different forcings which capture the main ideas in a simpler setting. For the entirety of the notes we work with an increasing sequence of large cardinals 〈κn | n < ω〉 with κ =def supn<ω κn. The large cardinal hypothesis that we use varies with the forcing. A recurring theme is the idea of a cell. A cell ...
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In order to present this result, we approach it by proving some preliminary theorems about different forcings which capture the main ideas in a simpler setting. For the entirety of the notes we work with an increasing sequence of large cardinals 〈κn | n < ω〉 with κ =def supn<ω κn. The large cardinal hypothesis that we use varies with the forcing. A recurring theme is the idea of a cell. A cell ...
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