On the powersets of singular cardinals in HOD
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- by Omer Ben-Neria, Moti Gitik, Itay Neeman and Spencer Unger PDF
- Proc. Amer. Math. Soc. 148 (2020), 1777-1789 Request permission
Abstract:
We prove that the assertion “There is a singular cardinal $\kappa$ such that for all $x \subseteq \kappa$, $\operatorname {HOD}_x$ does not contain the entire powerset of $\kappa$” is equiconsistent with the assertion that there is a cardinal $\kappa$ such that $\{o(\nu ) \mid \nu < \kappa \}$ is unbounded in $\kappa$.References
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Additional Information
- Omer Ben-Neria
- Affiliation: Institute of Mathematics The Hebrew University of Jerusalem, Jerusalem 91904, Israel
- MR Author ID: 1061476
- Email: omer.bn@mail.huji.ac.il
- Moti Gitik
- Affiliation: School of Mathematical Sciences, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Ramat Aviv 69978, Israel
- MR Author ID: 74045
- Email: gitik@post.tau.ac.il
- Itay Neeman
- Affiliation: Department of Mathematics, University of California, Los Angeles, Box 951555, Los Angeles, California 90095-1555
- MR Author ID: 366631
- Email: ineeman@math.ucla.edu
- Spencer Unger
- Affiliation: Institute of Mathematics The Hebrew University of Jerusalem, Jerusalem 91904, Israel
- MR Author ID: 983745
- Email: unger.spencer@mail.huji.ac.il
- Received by editor(s): September 2, 2018
- Received by editor(s) in revised form: August 30, 2019
- Published electronically: January 13, 2020
- Additional Notes: This work is based upon research supported by the National Science Foundation under Grants No. DMS-1363364, DMS-1764029 (Neeman), DMS-1700425 (Unger), and DMS-1800613 (Ben-Neria), and the Israel Science Foundation Grant No. 58/14 (Gitik).
- Communicated by: Heike Mildenberger
- © Copyright 2020 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 148 (2020), 1777-1789
- MSC (2010): Primary 03E10, 03E35, 03E45, 03E55
- DOI: https://doi.org/10.1090/proc/14913
- MathSciNet review: 4069214