Cardinalities of definable sets in superstructures over models
K. Zh. Kudaĭbergenov · Siberian Advances in Mathematics · 2010
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.