= Stable theory
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A <complete theory> $T$ is $\kappa$-stable, for an infinite <cardinal> $\kappa\geq|T|$, when $|S_1(A)|\leq\kappa$ for every parameter set $A$ of cardinality $\kappa$ in a model of $T$. Here $S_1(A)$ is the <type space> of complete one-variable types. The theory is stable if this holds for some such $\kappa$; it is omega-stable if it holds for $\aleph_0$.
For the theory of an infinite set with equality alone, a type over $A$ either names one element of $A$ or says that it differs from every member of $A$. There are only $|A|+1$ possibilities. By contrast, a <dense linear order without endpoints> has the <order property>, producing many types corresponding to cuts and hence instability. Stability measures the number of ways a new element can relate to existing parameters, rather than simply the number of models.
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