Hod mice and the Mouse Set Conjecture

DOI10.1090/memo/1111zbMath1403.03110OpenAlexW2039139196MaRDI QIDQ2944997

Grigor Sargsyan

Publication date: 9 September 2015

Published in: Memoirs of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/559e410624c76ca2d03cbacc6e8f7598ac11bec8

zbMATH Keywords

descriptive set theoryhod mouseinner model theorymouse

Mathematics Subject Classification ID

Descriptive set theory (03E15) Inner models, including constructibility, ordinal definability, and core models (03E45) Large cardinals (03E55) Determinacy principles (03E60)

Related Items (26)

Hod up to \(A D_{\mathbb{R}} + \Theta\) is measurable ⋮ A long pseudo-comparison of premice in \(L[x\)] ⋮ Determinacy from strong compactness of \(\omega_1\) ⋮ VARSOVIAN MODELS I ⋮ The comparison lemma ⋮ Woodin’s axiom (*), or Martin’s Maximum, or both? ⋮ Translation procedures in descriptive inner model theory ⋮ NEGATIVE RESULTS ON PRECIPITOUS IDEALS ON ⋮ Determinacy axioms and large cardinals ⋮ UNIVERSALLY BAIRE SETS AND GENERIC ABSOLUTENESS ⋮ The exact consistency strength of the generic absoluteness for the universally Baire sets ⋮ \(AD_{\mathbb{R}}\) implies that all sets of reals are \(\Theta\) universally Baire ⋮ DERIVED MODELS OF MICE BELOW THE LEAST FIXPOINT OF THE SOLOVAY SEQUENCE ⋮ A brief account of recent developments in inner model theory ⋮ Realizing an \(\mathrm{AD}^+\) model as a derived model of a premouse ⋮ Covering with Chang models over derived models ⋮ PFA and guessing models ⋮ Iterability for (transfinite) stacks ⋮ Square principles in \(\mathbb{P}_{\max}\) extensions ⋮ Supercompactness can be equiconsistent with measurability ⋮ PROVABLY GAMES ⋮ The definability of \(\mathbb{E}\) in self-iterable mice ⋮ SEALING OF THE UNIVERSALLY BAIRE SETS ⋮ The envelope of a pointclass under a local determinacy hypothesis ⋮ On the derived models of self-iterable universes ⋮ The AD+ conjecture and the continuum hypothesis

Cites Work

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• Descriptive set theory
• Cabal seminar 81-85. Proceedings, Caltech-UCLA logic seminar 1981-1985, Los Angeles, CA (USA)
• The axiom of determinacy, forcing axioms, and the nonstationary ideal
• Cabal Seminar 79-81. Proceedings, Caltech-UCLA Logic Seminar 1979-81
• Projectively well-ordered inner models
• HOD in natural models of \(\mathsf{AD}^+\)
• Descriptive inner model theory
• Non-tame Mice from Tame Failures of the Unique Branch Hypothesis
• Nontame mouse from the failure of square at a singular strong limit cardinal
• A classification of jump operators
• An Outline of Inner Model Theory
• Structural Consequences of AD
• Determinacy in L(ℝ)
• Large Cardinals from Determinacy
• SUITABLE EXTENDER MODELS I
• Deconstructing inner model theory
• Admissible Suslin cardinals in L(R)
• The self-iterability of L[E]
• Stacking mice
• On the determinacy of games on ordinals
• The Theory of Countable Analytical Sets
• Iteration Trees
• Measure and category in effective descriptive set theory
• Core models with more Woodin cardinals
• A universal extender model without large cardinals in V
• PFA implies AD^L(ℝ)
• THE MOUSE SET CONJECTURE FOR SETS OF REALS
• Inner models and large cardinals

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