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Pseudo-Prikry sequences


Author: Chris Lambie-Hanson
Journal: Proc. Amer. Math. Soc. 146 (2018), 4905-4920
MSC (2010): Primary 03E04, 03E05, 03E35
DOI: https://doi.org/10.1090/proc/13996
Published electronically: August 10, 2018
MathSciNet review: 3856157
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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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Additional Information

Chris Lambie-Hanson
Affiliation: Department of Mathematics, Bar-Ilan University, Ramat Gan 5290002, Israel – and – Department of Mathematics and Applied Mathematics, Virginia Commonwealth University, 1015 Floyd Avenue, Richmond, Virginia 23284
Email: lambiec@macs.biu.ac.il, cblambiehanso@vcu.edu

DOI: https://doi.org/10.1090/proc/13996
Received by editor(s): July 30, 2017
Received by editor(s) in revised form: September 25, 2017, and October 23, 2017
Published electronically: August 10, 2018
Additional Notes: We would like to thank Spencer Unger, conversations with whom led to the initial results of this paper. This work was completed while the author was a Lady Davis Postdoctoral Fellow at the Hebrew University of Jerusalem and a Coleman-Soref Postdoctoral Fellow at Bar-Ilan University; we would like to thank the Lady Davis Fellowship Trust, the Hebrew University, the Israel Science Foundation (grant #1630/14), and Bar-Ilan University. Finally, we would like to thank the anonymous referee for a number of helpful corrections and suggestions.
Communicated by: Heike Mildenberger
Article copyright: © Copyright 2018 American Mathematical Society