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.
Upward closure and amalgamation in the generic multiverse of a countable model of set theory
Chiron: A Set Theory with Types, Undefinedness, Quotation, and Evaluation
Another New Foundation: A Theory with Combined Concepts from Set Theory, Type Theory and Leśniewski's Mereology
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