A brief account of recent developments in inner model theory

DOI10.1090/conm/752/15136zbMath1496.03201OpenAlexW3036196109MaRDI QIDQ3299566

Nam Trang

Publication date: 23 July 2020

Published in: Trends in Set Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/conm/752/15136

Mathematics Subject Classification ID

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

Cites Work

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• Covering with universally Baire operators
• PFA and guessing models
• Square principles in \(\mathbb{P}_{\max}\) extensions
• The strength of choiceless patterns of singular and weakly compact cardinals
• The axiom of determinacy, forcing axioms, and the nonstationary ideal
• Inner models in the region of a Woodin limit of Woodin cardinals
• \(L(\mathbb{R}, \mu)\) is unique
• The envelope of a pointclass under a local determinacy hypothesis
• KWithout the Measurable
• Non-tame Mice from Tame Failures of the Unique Branch Hypothesis
• Nontame mouse from the failure of square at a singular strong limit cardinal
• Hod mice and the Mouse Set Conjecture
• Tame failures of the unique branch hypothesis and models of ADℝ + Θ is regular
• Sets constructed from sequences of measures: Revisited
• An Outline of Inner Model Theory
• SUITABLE EXTENDER MODELS I
• Determinacy from strong reflection
• The Ultrapower Axiom
• Scales in K(ℝ) at the end of a weak gap
• Inner Models and Ultrafilters In L(ℝ)
• Stacking mice
• A Proof of Projective Determinacy
• The core model
• Sets constructible from sequences of ultrafilters
• VARSOVIAN MODELS I
• HOD^L(ℝ) is a Core Model Below Θ
• A theorem of Woodin on mouse sets
• HODas a core model
• IN SEARCH OF ULTIMATE-LTHE 19TH MIDRASHA MATHEMATICAE LECTURES
• PFA implies AD^L(ℝ)
• Some applications of iterated ultrapowers in set theory
• The fine structure of the constructible hierarchy
• Inner models and large cardinals
• The domestic levels of \(K^c\) are iterable
• Equiconsistencies at subcompact cardinals

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