is the (set of Gödel numbers of the formulae in the) theory of the structure where U is a normal measure on the cardinal , and and are increasing enumerations of sets X and Y of ordinals with which are indiscernibles for , in the sense that the truth value of
is independent of the choice of the increasing sequences from X and from
was first defined by Solovay, who showed that if there were to measurable cardinals , with then exists [see A. R. D. Mathias, Period. Math. Hung. 10, 109-175 (1979; Zbl 0417.03021)]. The set plays a similar role for inner models with a measurable cardinal as plays for L.
Various results about have appeared in the literature. However the survey paper under review is the first detailed presentation of the theory of . Section 1 defines and contains the appropriate Ehrenfeucht-Mostowski theory and shows that sufficiently strong large cardinal hypotheses generate models L[U] with indiscernibles. In section 2 connections are established between classes of indiscernibles for various of these models. Finally, section 3 reviews various characterizations of the existence of .