The ground axiom

DOI10.2178/jsl/1203350787zbMath1135.03018arXivmath/0609064OpenAlexW2139907287WikidataQ114005168 ScholiaQ114005168MaRDI QIDQ5444701

Jonas Reitz

Publication date: 25 February 2008

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

Full work available at URL: https://arxiv.org/abs/math/0609064

zbMATH Keywords

forcingcodingordinal definabilitythe Bedrock Axiomthe Ground Axiom

Mathematics Subject Classification ID

Consistency and independence results (03E35) Inner models, including constructibility, ordinal definability, and core models (03E45) Other set-theoretic hypotheses and axioms (03E65)

Related Items (29)

Coding into HOD via normal measures with some applications ⋮ Accessing the switchboard via set forcing ⋮ THE SET-THEORETIC MULTIVERSE ⋮ Inner-model reflection principles ⋮ STEEL’S PROGRAMME: EVIDENTIAL FRAMEWORK, THE CORE AND ULTIMATE-L ⋮ Large cardinals at the brink ⋮ The grounded Martin's axiom ⋮ Inner models with large cardinal features usually obtained by forcing ⋮ The downward directed grounds hypothesis and very large cardinals ⋮ Inner mantles and iterated HOD ⋮ Subcomplete forcing principles and definable well‐orders ⋮ TWO ARGUMENTS AGAINST THE GENERIC MULTIVERSE ⋮ The ground axiom is consistent with V $\neq $ HOD ⋮ Extendible cardinals and the mantle ⋮ More on HOD-supercompactness ⋮ Resurrection axioms and uplifting cardinals ⋮ Forcing, Multiverse and Realism ⋮ The Ultrapower Axiom ⋮ The consistency of level by level equivalence with $V = {\rm HOD}$, the Ground Axiom, and instances of square and diamond ⋮ The least weakly compact cardinal can be unfoldable, weakly measurable and nearly \(\theta\)-supercompact ⋮ Indestructibility, HOD, and the Ground Axiom ⋮ Set-theoretic blockchains ⋮ Some Second Order Set Theory ⋮ Superstrong and other large cardinals are never Laver indestructible ⋮ Laver and set theory ⋮ Set-theoretic geology ⋮ A RECONSTRUCTION OF STEEL’S MULTIVERSE PROJECT ⋮ Choiceless Löwenheim-Skolem property and uniform definability of grounds ⋮ MORE ON THE PRESERVATION OF LARGE CARDINALS UNDER CLASS FORCING

Cites Work

• Set theory. An introduction to independence proofs
• Making the supercompactness of \(\nu\) indestructible under \(\nu\)-directed closed forcing
• Fine structure and class forcing
• Extensions with the approximation and cover properties have no new large cardinals
• Powers of regular cardinals
• Consistency results about ordinal definability

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