Woodin’s axiom (*), or Martin’s Maximum, or both?

DOI10.1090/conm/690/13868zbMath1423.03198OpenAlexW4235472892MaRDI QIDQ5351855

Ralf-Dieter Schindler

Publication date: 30 August 2017

Published in: Foundations of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/conm/690/13868

zbMATH Keywords

Martin's maximum\({\mathbb P}_{\mathrm{max}}\) forcing

Mathematics Subject Classification ID

Inner models, including constructibility, ordinal definability, and core models (03E45) Large cardinals (03E55) Other set-theoretic hypotheses and axioms (03E65) Determinacy principles (03E60) Generic absoluteness and forcing axioms (03E57)

Related Items (2)

On a class of maximality principles ⋮ Martin's maximum\(^{++}\) implies Woodin's axiom \((*)\)

Cites Work

• Bounded Martin's maximum with an asterisk
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• Martin's maximum, saturated ideals, and nonregular ultrafilters. I
• The axiom of determinacy, forcing axioms, and the nonstationary ideal
• Martin's Maximum and the \(\mathbb{P}_{\max}\) Axiom \((*)\)
• The envelope of a pointclass under a local determinacy hypothesis
• Set theory. Exploring independence and truth
• Woodin's axiom (*), bounded forcing axioms, and precipitous ideals on ω₁
• Hod mice and the Mouse Set Conjecture
• An Outline of Inner Model Theory
• Large Cardinals from Determinacy
• Forcing over Models of Determinacy
• Two Consequences of Determinacy Consistent with Choice
• The self-iterability of L[E]
• Increasing u₂ by a stationary set preserving forcing
• A Proof of Projective Determinacy
• Iteration Trees
• A theorem of Woodin on mouse sets
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