Stable theory

Summary

A complete theory is stable when its models have few types. For some infinite cardinal $\lambda$, every parameter set of size $\lambda$ has at most $\lambda$ complete types over it. Equivalently, no formula can define an infinite linear order on tuples, a condition called the order property. Stable theories, introduced and developed by Saharon Shelah, admit a good theory of independence and dimension. Algebraically closed fields, vector spaces and modules give stable theories, while dense linear orders and real closed fields do not.