Large cardinals need not be large in HOD

DOI10.1016/j.apal.2015.07.004zbMath1373.03109arXiv1407.6335OpenAlexW2155287324MaRDI QIDQ490870

Sy-David Friedman, Joel David Hamkins, Yong Cheng

Publication date: 21 August 2015

Published in: Annals of Pure and Applied Logic (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1407.6335

zbMATH Keywords

forcingabsolutenesslarge cardinalsHOD

Mathematics Subject Classification ID

Consistency and independence results (03E35) Inner models, including constructibility, ordinal definability, and core models (03E45) Large cardinals (03E55) Other aspects of forcing and Boolean-valued models (03E40)

Related Items

Indestructibility properties of Ramsey and Ramsey-like cardinals, Indestructibility properties of remarkable cardinals, STRUCTURAL PROPERTIES OF THE STABLE CORE, The Hypothesis and a supercompact cardinal, Strongly compact cardinals and ordinal definability, Strong combinatorial principles and level by level equivalence, More on HOD-supercompactness, The consistency of level by level equivalence with $V = {\rm HOD}$, the Ground Axiom, and instances of square and diamond

Cites Work

• Unnamed Item
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• Easton's theorem in the presence of Woodin cardinals
• On extendible cardinals and the GCH
• The least weakly compact cardinal can be unfoldable, weakly measurable and nearly \(\theta\)-supercompact
• Indestructible strong unfoldability
• On certain indestructibility of strong cardinals and a question of Hajnal
• Making the supercompactness of \(\nu\) indestructible under \(\nu\)-directed closed forcing
• Destruction or preservation as you like it
• The lottery preparation
• Rank-into-rank hypotheses and the failure of GCH
• SQUARES, SCALES AND STATIONARY REFLECTION
• The Stable core
• HOD-supercompactness, Indestructibility, and Level by Level Equivalence
• Ramsey-like cardinals
• Ramsey-like cardinals II
• SUITABLE EXTENDER MODELS I
• Large cardinals and definable well-orders on the universe
• Saturated ideals
• Variations on ◊
• 0^# and inner models
• Set Theory
• Extensions with the approximation and cover properties have no new large cardinals
• Tall cardinals
• Consistency results about ordinal definability
• Collapsing the cardinals of HOD
• The wholeness axioms and V=HOD
• Superstrong and other large cardinals are never Laver indestructible