SUITABLE EXTENDER MODELS I

DOI10.1142/S021906131000095XzbMath1247.03110MaRDI QIDQ3094356

W. Hugh Woodin

Publication date: 24 October 2011

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

zbMATH Keywords

extenderinner modelssupercompact cardinaliteration tree\(\Omega\)-conjecture

Mathematics Subject Classification ID

Consistency and independence results (03E35) Inner models, including constructibility, ordinal definability, and core models (03E45) Large cardinals (03E55) Other set-theoretic hypotheses and axioms (03E65) Axiom of choice and related propositions (03E25) Determinacy principles (03E60)

Related Items (42)

SUITABLE EXTENDER MODELS II: BEYOND ω-HUGE ⋮ On -Strongly Measurable Cardinals ⋮ IN SEARCH OF ULTIMATE-LTHE 19TH MIDRASHA MATHEMATICAE LECTURES ⋮ AXIOM I₀ AND HIGHER DEGREE THEORY ⋮ The enriched stable core and the relative rigidity of HOD ⋮ SOME APPLICATIONS OF SUPERCOMPACT EXTENDER BASED FORCINGS TO HOD ⋮ Hod mice and the Mouse Set Conjecture ⋮ Critical cardinals ⋮ Tame failures of the unique branch hypothesis and models of ADℝ + Θ is regular ⋮ Measurable cardinals and choiceless axioms ⋮ Large cardinals at the brink ⋮ The relative strengths of fragments of Martin's axiom ⋮ The Hypothesis and a supercompact cardinal ⋮ How many real numbers are there? ⋮ Homogeneous changes in cofinalities with applications to HOD ⋮ Generic at ⋮ A premouse inheriting strong cardinals from \(V\) ⋮ UNIVERSALLY BAIRE SETS AND GENERIC ABSOLUTENESS ⋮ Set theory. Abstracts from the workshop held January 9--15, 2022 ⋮ Consecutive singular cardinals and the continuum function ⋮ Combinatorial properties and dependent choice in symmetric extensions based on Lévy collapse ⋮ More on HOD-supercompactness ⋮ Covering with universally Baire operators ⋮ A brief account of recent developments in inner model theory ⋮ Large cardinals need not be large in HOD ⋮ N-BERKELEY CARDINALS AND WEAK EXTENDER MODELS ⋮ BERKELEY CARDINALS AND THE STRUCTURE OF L(Vδ+1) ⋮ I0 and rank-into-rank axioms ⋮ The long extender algebra ⋮ Laver and set theory ⋮ Equiconsistencies at subcompact cardinals ⋮ The weak ultrafilter axiom ⋮ LARGE CARDINALS BEYOND CHOICE ⋮ CLASSES OF BARREN EXTENSIONS ⋮ DEPENDENT CHOICE, PROPERNESS, AND GENERIC ABSOLUTENESS ⋮ 𝖲𝖾𝖺𝗅𝗂𝗇𝗀 from iterability ⋮ PROVABLY GAMES ⋮ How Woodin changed his mind: new thoughts on the continuum hypothesis ⋮ Choiceless Löwenheim-Skolem property and uniform definability of grounds ⋮ Boolean-valued second-order logic ⋮ The envelope of a pointclass under a local determinacy hypothesis ⋮ MORE ON THE PRESERVATION OF LARGE CARDINALS UNDER CLASS FORCING

Cites Work

• On HOD-supercompactness
• Descriptive set theory
• Inner models in the region of a Woodin limit of Woodin cardinals
• Certain very large cardinals are not created in small forcing extensions
• Counterexamples to the unique and cofinal branches hypotheses
• The well-foundedness of the Mitchell order

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