DEPENDENT CHOICE, PROPERNESS, AND GENERIC ABSOLUTENESS

DOI10.1017/S1755020320000143MaRDI QIDQ5001556

David Asperó, Asaf Karagila

Publication date: 22 July 2021

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

Full work available at URL: https://arxiv.org/abs/1806.04077

zbMATH Keywords

axiom of choicePFAforcing axiomsgeneric absolutenessproper forcingChang model

Mathematics Subject Classification ID

Philosophical and critical aspects of logic and foundations (03A05) Consistency and independence results (03E35) Large cardinals (03E55) Axiom of choice and related propositions (03E25) Generic absoluteness and forcing axioms (03E57)

Related Items

Sequential and distributive forcings without choice ⋮ Determinacy and regularity properties for idealized forcings ⋮ Preserving Dependent Choice ⋮ Properness under closed forcing ⋮ Choiceless chain conditions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Intermediate submodels and generic extensions in set theory
• Measurable cardinals and the continuum hypothesis
• Critical cardinals
• A model of set-theory in which every set of reals is Lebesgue measurable
• Category forcings, 𝑀𝑀⁺⁺⁺, and generic absoluteness for the theory of strong forcing axioms
• Proper Forcing
• SUITABLE EXTENDER MODELS I
• Elementary embeddings and infinitary combinatorics
• On generic extensions without the axiom of choice
• C.c.c. forcing without combinatorics
• Supercompact cardinals, sets of reals, and weakly homogeneous trees
• Los' Theorem and the Boolean Prime Ideal Theorem Imply the Axiom of Choice
• Adding dependent choice
• Small forcing makes any cardinal superdestructible
• The Bristol model: An abyss called a Cohen real
• Fragments of Martin's Maximum in generic extensions
• IN SEARCH OF ULTIMATE-LTHE 19TH MIDRASHA MATHEMATICAE LECTURES
• Preserving Dependent Choice
• The modal logic of forcing
• SET MAPPING REFLECTION
• The axiom of choice