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MORE ON BLURRY HOD

Part of: Set theory

Published online by Cambridge University Press:  07 December 2023

GUNTER FUCHS Open the ORCID record for GUNTER FUCHS [Opens in a new window]
GUNTER FUCHS*
Affiliation:
THE COLLEGE OF STATEN ISLAND THE CITY UNIVERSITY OF NEW YORK (CUNY) 2800 VICTORY BOULEVARD STATEN ISLAND NY 10314, USA and THE GRADUATE CENTER THE CITY UNIVERSITY OF NEW YORK (CUNY) 365 5TH AVENUE, NEW YORK NY 10016, USA URL: www.math.csi.cuny.edu/~fuchs
*
E-mail: gunter.fuchs@csi.cuny.edu
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Abstract

I continue the study of the blurry HOD hierarchy. The technically most involved result is that the theory ZFC + “$\aleph _\omega $ is a strong limit cardinal and $\aleph _{\omega +1}$ is the least leap” is equiconsistent with the theory ZFC + “there is a measurable cardinal.”

Keywords

Ordinal definabilityforcinglarge cardinalsinner models

MSC classification

Primary: 03E35: Consistency and independence results 03E40: Other aspects of forcing and Boolean-valued models 03E45: Inner models, including constructibility, ordinal definability, and core models 03E47: Other notions of set-theoretic definability 03E55: Large cardinals

Information

Type
Article
Information
The Journal of Symbolic Logic , Volume 90 , Issue 2 , June 2025 , pp. 822 - 853
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

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