Type

Summary

In model theory, a type is a set of formulas in some free variables that is consistent with a theory. It describes the possible behaviour of a tuple of elements. A complete type gives a full first-order description of a tuple: every formula or its negation belongs to it. A type is realized in a model when some tuple of the model satisfies all its formulas, and omitted otherwise. Types are the basic tool for comparing models, and counting them leads to saturated models, categoricity and stability.