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“Models of set theory” is a category for books that study the mathematical structures (models) in which the axioms of set theory—typically ZF/ZFC and their extensions—hold, and how these models relate to one another. Works in this area explore techniques such as forcing and generic extensions, inner models (like Gödel’s constructible universe L and core model theory), large cardinal axioms and elementary embeddings, consistency and independence results (e.g., the Continuum Hypothesis), absoluteness and reflection principles, and connections to descriptive set theory and combinatorics. The category includes accessible introductions to the landscape of possible set-theoretic universes, expositions of Gödel–Cohen style results, and advanced research monographs on inner model theory, forcing axioms, determinacy, and the fine structure of models.

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