Ehrenfeucht–Mostowski theorem
In model theory, a field within mathematical logic, the Ehrenfeucht–Mostowski theorem gives conditions for the existence of a model with indiscernibles.
Statement
A linearly ordered set X is called a set of indiscernibles of a model if the truth of a statement about elements of X depends only on their order.The Ehrenfeucht–Mostowski theorem states that
if T is a theory with an infinite model, then there is a model of T containing any given linearly ordered set X as a set of indiscernibles.
The proof uses Ramsey's theorem.