Preserving Dependent Choice

DOI10.4064/ba8169-12-2018zbMath1479.03021arXiv1810.11301OpenAlexW3099875334WikidataQ128480831 ScholiaQ128480831MaRDI QIDQ5382834

Asaf Karagila

Publication date: 18 June 2019

Published in: Bulletin of the Polish Academy of Sciences Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1810.11301

zbMATH Keywords

dependent choicesymmetric extensionsthe axiom of choice

Mathematics Subject Classification ID

Consistency and independence results (03E35) Axiom of choice and related propositions (03E25)

Related Items (8)

TAKING REINHARDT’S POWER AWAY ⋮ Sequential and distributive forcings without choice ⋮ Remarks on Gitik's model and symmetric extensions on products of the Lévy collapse ⋮ Combinatorial properties and dependent choice in symmetric extensions based on Lévy collapse ⋮ The Morris model ⋮ REALIZING REALIZABILITY RESULTS WITH CLASSICAL CONSTRUCTIONS ⋮ DEPENDENT CHOICE, PROPERNESS, AND GENERIC ABSOLUTENESS ⋮ Choiceless chain conditions

Cites Work

• Sacks forcing and the total failure of Martin's axiom
• Six impossible rings
• On some questions concerning strong compactness
• Injectivity, Projectivity, and the Axiom of Choice
• On the Effectivity of Some Field Constructions
• The Bristol model: An abyss called a Cohen real
• Hamel bases and well–ordering the continuum
• ITERATING SYMMETRIC EXTENSIONS
• DEPENDENT CHOICE, PROPERNESS, AND GENERIC ABSOLUTENESS
• Spectra of uniformity
• Embedding orders into the cardinals with \mathsf DC_κ
• The axiom of choice

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