The downward directed grounds hypothesis and very large cardinals

DOI10.1142/S021906131750009XzbMath1423.03191arXiv1707.05132MaRDI QIDQ4596665

Toshimichi Usuba

Publication date: 4 December 2017

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

Full work available at URL: https://arxiv.org/abs/1707.05132

zbMATH Keywords

forcing methodlarge cardinalset-theoretic geologygeneric multiversedownward directed grounds hypothesis

Mathematics Subject Classification ID

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

Related Items (19)

THE MODAL LOGIC OF SET-THEORETIC POTENTIALISM AND THE POTENTIALIST MAXIMALITY PRINCIPLES ⋮ On a class of maximality principles ⋮ VARSOVIAN MODELS I ⋮ Model theoretic characterizations of large cardinals ⋮ Inner-model reflection principles ⋮ STEEL’S PROGRAMME: EVIDENTIAL FRAMEWORK, THE CORE AND ULTIMATE-L ⋮ Choice principles in local mantles ⋮ Inner mantles and iterated HOD ⋮ Subcomplete forcing principles and definable well‐orders ⋮ TWO ARGUMENTS AGAINST THE GENERIC MULTIVERSE ⋮ Extendible cardinals and the mantle ⋮ The Ultrapower Axiom ⋮ On the Set-Generic Multiverse ⋮ Can all things be counted? ⋮ Set-theoretic blockchains ⋮ UNIVERSISM AND EXTENSIONS OF V ⋮ A RECONSTRUCTION OF STEEL’S MULTIVERSE PROJECT ⋮ Choiceless Löwenheim-Skolem property and uniform definability of grounds ⋮ IN INNER MODELS WITH WOODIN CARDINALS

Cites Work

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• The long extender algebra
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• Characterization of generic extensions of models of set theory
• Extensions with the approximation and cover properties have no new large cardinals
• ON THE SET-GENERIC MULTIVERSE
• The ground axiom
• Superstrong and other large cardinals are never Laver indestructible

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