The Geometry of Minimal Types in Theories Interpretable in O-minimal
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چکیده
Definition 1.3. Let C be a monster model of a theory interpretable in o-minimal structure. • A set φ(x) is finite by o-minimal if there is some definable equivalence relation E with finite classes and domain φ(C and a definable binary relation < such that (φ(C)/E,<) together with the C-induced structure is an ominimal ordered set. • A type p(x) is finite by o-minimal if there is some finite by o-minimal formula φ(x) such that p(x) ∪ {φ(x)} is non algebraic. • A type p(x) is an almost generic extension of θ(y) if there is some formula φ(x) and some equivalence relation E with finite classes such that p(x) is a generic extension of φ(x) and θ(y) := φ(x)/E.
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