Pseudo-Prikry sequences

Lambie-Hanson, Chris

doi:10.1090/proc/13996

Pseudo-Prikry sequences
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by Chris Lambie-Hanson PDF

Proc. Amer. Math. Soc. 146 (2018), 4905-4920 Request permission

Abstract:

We generalize results of Gitik, Džamonja-Shelah, and Magidor-Sinapova on the existence of pseudo-Prikry sequences, which are sequences that approximate the behavior of the generic objects introduced by Prikry-type forcings, in outer models of set theory. Such sequences play an important role in the study of singular cardinal combinatorics by placing restrictions on the type of behavior that can consistently be obtained in outer models. In addition, we provide results about the existence of diagonal pseudo-Prikry sequences, which approximate the behavior of the generic objects introduced by diagonal Prikry-type forcings. Our proof techniques are substantially different from those of previous results and rely on an analysis of PCF-theoretic objects in the outer model.

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