Bi-colored Expansions of Geometric Theories
This talk is concerned with Bi-colored expansions of geometric theories in the light of the Fraisse-Hrushovski construction method. Substructures of models of a geometric T are expanded by a color predicate p, where the dimension function associated with the pre-geometry of the T-algebraic closure operator together with a real number 0<α<1 give rise to a pre-dimension function δα. Imposing certain natural conditions on T, enables us to introduce a complete axiomatization Tα for the class of rich structures. It follows that if T is a dependent theory (NIP) then so is Tα. We further prove that whenever α is rational the strong dependence transfers to Tα. We are further able to show that if T defines a linear order and α is irrational then Tα is not strongly dependent. This is a joint work with S.Jalili and M.Khani