Infinite forcing and the generic multiverse

DOI10.1007/s11225-019-09851-8zbMath1484.03111arXiv1903.09960OpenAlexW2913228604WikidataQ128413669 ScholiaQ128413669MaRDI QIDQ2307303

Giorgio Venturi

Publication date: 27 March 2020

Published in: Studia Logica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1903.09960

zbMATH Keywords

forcingbounded forcing axiomsgenericitygeneric absolutenessRobinson's infinite forcing

Mathematics Subject Classification ID

Consistency and independence results (03E35) Model-theoretic forcing (03C25) Generic absoluteness and forcing axioms (03E57)

Cites Work

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• Forcing, arithmetic, division rings
• Robinson forcing is not absolute
• The axiom of determinacy, forcing axioms, and the nonstationary ideal
• Bounded forcing axioms as principles of generic absoluteness
• Resurrection axioms and uplifting cardinals
• Set-theoretic geology
• Category forcings, 𝑀𝑀⁺⁺⁺, and generic absoluteness for the theory of strong forcing axioms
• The hyperuniverse program
• THE SET-THEORETIC MULTIVERSE
• A simple maximality principle
• Skolem and pessimism about proof in mathematics

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