Infinite Forcing and the Generic Multiverse
In this article we present a technique for selecting models of set theory that are complete in a model-theoretic sense. Specifically, we will apply Robinson infinite forcing to the collections of models of ZFC obtained by Cohen forcing. This technique will be used to suggest a unified perspective on generic absoluteness principles.
KeywordsSet theory Genericity Forcing Robinson’s infinite forcing Bounded Forcing Axioms Generic absoluteness
Mathematics Subject Classification03E35 03E57 03C25
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We thank an anonymous referee for the careful reading, comments, and criticisms. We acknowledge the kind support of FAPESP in the form of the Jovem Pesquisador grant n. 2016/25891-3.
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