Ultraproduct Construction

A model-theoretic construction that forms a new structure by taking the Cartesian product of a family of structures and quotienting by an ultrafilter, used to transfer properties and produce limit-like models.

A model-theoretic construction that forms a new structure from a family (A_i)_{i∈I} of structures of the same signature and an ultrafilter U on I by taking the Cartesian product modulo the equivalence relation that identifies two sequences when they agree on a set in U; first-order properties satisfied on a U-large set transfer to the ultraproduct.