Cardinalities of definable sets in superstructures over models

2010

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DOI 10.3103/s1055134410010025
Data confidence 70 medium
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Abstract

We introduce the notion of a superstructure over a model. This is a generalization of the notion of the hereditarily finite superstructure ℍ $$ \mathbb{F}\mathfrak{M} $$ over a model $$ \mathfrak{M} $$ . We consider the question on cardinalities of definable (interpretable) sets in superstructures over λ-homogeneous and λ-saturated models.