Scott formula
= Scott formula
{c}
{title2=$\phi_{\bar a}^{\alpha}(\bar x)$}
A Scott formula describes a finite <tuple> at a transfinite stage of the <back-and-forth method>. Stage zero specifies the complete atomic description; successor stages specify matching one-element extensions in both directions; limit stages conjoin the earlier descriptions. For a countable structure the equivalences on its finite <tuples> stabilize at a countable <ordinal>.