Woodin's axiom (*), bounded forcing axioms, and precipitous ideals on ω1

DOI10.2178/jsl/1333566633zbMath1250.03111OpenAlexW2031165885WikidataQ114005165 ScholiaQ114005165MaRDI QIDQ2892671

Benjamin Claverie, Ralf-Dieter Schindler

Publication date: 19 June 2012

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

Full work available at URL: https://projecteuclid.org/euclid.jsl/1333566633

Mathematics Subject Classification ID

Inner models, including constructibility, ordinal definability, and core models (03E45) Other aspects of forcing and Boolean-valued models (03E40) Generic absoluteness and forcing axioms (03E57)

Related Items (20)

Compactness versus hugeness at successor cardinals ⋮ On a class of maximality principles ⋮ In memoriam: James Earl Baumgartner (1943--2011) ⋮ Weak saturation properties and side conditions ⋮ Woodin’s axiom (*), or Martin’s Maximum, or both? ⋮ THE DIAGONAL STRONG REFLECTION PRINCIPLE AND ITS FRAGMENTS ⋮ NEGATIVE RESULTS ON PRECIPITOUS IDEALS ON ⋮ How many real numbers are there? ⋮ When cardinals determine the power set: inner models and Härtig quantifier logic ⋮ Σ₁(κ)-DEFINABLE SUBSETS OF H(κ⁺) ⋮ Diagonal reflections on squares ⋮ Consistency strength of higher Chang's conjecture, without CH ⋮ HIERARCHIES OF FORCING AXIOMS, THE CONTINUUM HYPOTHESIS AND SQUARE PRINCIPLES ⋮ Generic Vopěnka's principle, remarkable cardinals, and the weak proper forcing axiom ⋮ Canonical fragments of the strong reflection principle ⋮ Martin's maximum\(^{++}\) implies Woodin's axiom \((*)\) ⋮ Virtual large cardinals ⋮ Bounded Martin's maximum with an asterisk ⋮ DOWNWARD TRANSFERENCE OF MICE AND UNIVERSALITY OF LOCAL CORE MODELS ⋮ ARONSZAJN TREE PRESERVATION AND BOUNDED FORCING AXIOMS

Cites Work

• \(\Pi_2\) consequences of \(\mathsf{BMM}+\mathsf{NS}_{\omega_1}\) is precipitous and the semiproperness of stationary set preserving forcings
• A criterion for coarse iterability
• The strength of choiceless patterns of singular and weakly compact cardinals
• Iterated forcing and normal ideals on \(\omega _ 1\)
• The axiom of determinacy, forcing axioms, and the nonstationary ideal
• Bounded forcing axioms as principles of generic absoluteness
• Projectively well-ordered inner models
• Combinatorial principles in the core model for one Woodin cardinal
• Weak covering without countable closure
• Proper forcing and remarkable cardinals II
• Square in Core Models
• An Outline of Inner Model Theory
• The self-iterability of L[E]
• The maximality of the core model
• The fine structure of the constructible hierarchy
• CHARACTERIZATION OF □_κ IN CORE MODELS

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