= Model-theoretic ultralimit
An ultralimit is the direct limit of a chain of structures formed by taking successive <ultrapowers> along their diagonal <elementary embeddings>. At limit stages use the <elementary chain theorem>. This is a different concept from a topological <ultrafilter limit>. Alternating relative ultrapower embeddings constructs isomorphic ultralimits of any two elementarily equivalent structures, without requiring the stronger single-ultrapower isomorphism theorem.
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