Second order arithmetic as the model companion of set theory

DOI10.1007/s00153-022-00831-9OpenAlexW4283397374MaRDI QIDQ2700811

Matteo Viale, Giorgio Venturi

Publication date: 27 April 2023

Published in: Archive for Mathematical Logic (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1909.13372

zbMATH Keywords

forcinglarge cardinalsgeneric absolutenessmodel companionRobinson infinite forcing

Mathematics Subject Classification ID

Large cardinals (03E55) Quantifier elimination, model completeness, and related topics (03C10) Model-theoretic forcing (03C25) Generic absoluteness and forcing axioms (03E57)

Cites Work

• Multiverse conceptions in set theory
• Forcing, arithmetic, division rings
• Category forcings, 𝑀𝑀⁺⁺⁺, and generic absoluteness for the theory of strong forcing axioms
• Forcing over Models of Determinacy
• Forcing, Multiverse and Realism
• The Model Companion of ZF
• Absoluteness via resurrection
• Set Theory
• On Forms of Justification in Set Theory
• Martin's maximum revisited
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