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Statements

Subject Item

dbr:Inner_model_theory

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Inner model theory

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In set theory, inner model theory is the study of certain models of ZFC or some fragment or strengthening thereof. Ordinarily these models are transitive subsets or subclasses of the von Neumann universe V, or sometimes of a generic extension of V. Inner model theory studies the relationships of these models to determinacy, large cardinals, and descriptive set theory. Despite the name, it is considered more a branch of set theory than of model theory.

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dbr:Solovay_model dbr:Continuum_hypothesis dbr:Constructible_universe dbr:Springer_Science+Business_Media dbr:Zero_dagger dbr:Set_theory dbr:Subset dbr:Kurt_Gödel dbr:Transitive_set dbr:Forcing_(mathematics) dbc:Inner_model_theory dbr:Diamond_principle dbr:Zermelo–Fraenkel_set_theory dbr:Determinacy dbr:L(R) dbr:Model_theory dbr:Subclass_(set_theory) dbr:Axiom_of_constructibility dbr:Ordinal_definable_set dbr:Class_(set_theory) dbr:Consistency dbr:Inner_model dbr:Core_model dbr:Large_cardinal dbr:Descriptive_set_theory dbr:Equiconsistency dbr:Von_Neumann_universe

dbo:abstract

In set theory, inner model theory is the study of certain models of ZFC or some fragment or strengthening thereof. Ordinarily these models are transitive subsets or subclasses of the von Neumann universe V, or sometimes of a generic extension of V. Inner model theory studies the relationships of these models to determinacy, large cardinals, and descriptive set theory. Despite the name, it is considered more a branch of set theory than of model theory.

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