Large cardinals and definable well-orders on the universe

DOI10.2178/jsl/1243948331zbMath1166.03029arXiv0711.2591OpenAlexW2045982637WikidataQ61834610 ScholiaQ61834610MaRDI QIDQ3630583

Andrew D. Brooke-Taylor

Publication date: 4 June 2009

Published in: The Journal of Symbolic Logic (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0711.2591

zbMATH Keywords

codingGCHvery large cardinalsdefinable well-orderreverse Easton forcing iteration

Mathematics Subject Classification ID

Consistency and independence results (03E35) Inner models, including constructibility, ordinal definability, and core models (03E45) Large cardinals (03E55)

Related Items (14)

Coding into HOD via normal measures with some applications ⋮ Accessing the switchboard via set forcing ⋮ Subcompact cardinals, squares, and stationary reflection ⋮ Mutually embeddable models of ZFC ⋮ Inner models with large cardinal features usually obtained by forcing ⋮ Indestructibility of Vopěnka's principle ⋮ Strong combinatorial principles and level by level equivalence ⋮ The consistency of level by level equivalence with $V = {\rm HOD}$, the Ground Axiom, and instances of square and diamond ⋮ Large cardinals need not be large in HOD ⋮ Pointwise definable models of set theory ⋮ HOD, V AND THE GCH ⋮ Large cardinals and locally defined well-orders of the universe ⋮ Set-theoretic geology ⋮ MORE ON THE PRESERVATION OF LARGE CARDINALS UNDER CLASS FORCING

Cites Work

• Large cardinals and locally defined well-orders of the universe
• The axiom of determinacy, forcing axioms, and the nonstationary ideal
• Fine structure and class forcing
• Indexed squares
• The lottery preparation
• SQUARES, SCALES AND STATIONARY REFLECTION
• Gap Forcing: Generalizing the Lévy-Solovay Theorem
• The wholeness axioms and V=HOD

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