Diagonal supercompact Radin forcing

Omer Ben-Neria; Chris Lambie-Hanson; Spencer Unger

doi:10.1016/j.apal.2020.102828

Diagonal supercompact Radin forcing

Omer Ben-Neria, Chris Lambie-Hanson, Spencer Unger^*

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

Motivated by the goal of constructing a model in which there are no κ-Aronszajn trees for any regular κ>ℵ₁, we produce a model with many singular cardinals where both the singular cardinals hypothesis and weak square fail.

Original language	American English
Article number	102828
Journal	Annals of Pure and Applied Logic
Volume	171
Issue number	10
DOIs	https://doi.org/10.1016/j.apal.2020.102828
State	Published - Dec 2020

Bibliographical note

Funding Information:
This research was conducted while the second author was a Lady Davis Postdoctoral Fellow. The author would like to thank the Lady Davis Fellowship Trust and the Hebrew University of Jerusalem . The third author was partially supported by NSF DMS-1700425 . We would also like to thank the anonymous referee, who made a number of helpful corrections and suggestions that substantially improved the paper.

Publisher Copyright:
© 2020 Elsevier B.V.

Keywords

Radin forcing
Supercompact cardinals
Weak square

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10.1016/j.apal.2020.102828

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abstract = "Motivated by the goal of constructing a model in which there are no κ-Aronszajn trees for any regular κ>ℵ1, we produce a model with many singular cardinals where both the singular cardinals hypothesis and weak square fail.",

keywords = "Radin forcing, Supercompact cardinals, Weak square",

author = "Omer Ben-Neria and Chris Lambie-Hanson and Spencer Unger",

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AU - Lambie-Hanson, Chris

AU - Unger, Spencer

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N2 - Motivated by the goal of constructing a model in which there are no κ-Aronszajn trees for any regular κ>ℵ1, we produce a model with many singular cardinals where both the singular cardinals hypothesis and weak square fail.

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KW - Radin forcing

KW - Supercompact cardinals

KW - Weak square

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JO - Annals of Pure and Applied Logic

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ER -

Diagonal supercompact Radin forcing

Abstract

Bibliographical note

Keywords

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