model theory In mathematical logic, model theory is the study of the relationship between theory (mathematical logic), formal theories (a collection of Sentence (mathematical logic), sentences in a formal language expressing statements about a Structure (mat ...

, a field within

mathematical logic Mathematical logic is the study of Logic#Formal logic, formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory (also known as computability theory). Research in mathematical logic com ...

, 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.

Applications

The Ehrenfeucht–Mostowski is used to construct models with many automorphisms. It is also used in the theory of zero sharp to construct indiscernibles in the constructible universe.

References

* {{DEFAULTSORT:Ehrenfeucht-Mostowski theorem Model theory Theorems in the foundations of mathematics