 Ehrenfeucht–Mostowski theorem

If a first-order theory has an infinite model, then for every total order $I$ it has an elementary extension containing distinct order indiscernibles $(a_i{)}_{i\in I}$ whose Skolem hull is a model of the theory. Every order automorphism of $I$ extends uniquely to an automorphism of that hull.

The Ehrenfeucht–Mostowski theorem is a result in model theory, a branch of mathematical logic that studies the relationships between formal languages and their interpretations or models. This theorem addresses the preservation of certain properties in structures when extending or modifying them.