= Atomic model without finite-tuple homogeneity
An equivalence-relation <first-order structure> with exactly two infinite classes, one <countable> and one uncountable, is atomic but lacks <finite-tuple homogeneity>. Its <first-order theory> has <quantifier elimination>: a new point is either assigned a previously used class or an available unused class, and can avoid finitely many forbidden points in that infinite class. Finite equality-and-equivalence patterns therefore isolate all <tuple> <partial types>. All elements have the same <complete one-type>, but no automorphism exchanges the two differently sized classes.
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