Abstract:

The thesis is a research about nonisolation properties of superstable types over finite domains in general. Two notions of nonisoltions, the notion of eventualstrong (i.e. esn) and the notion of internal are introduced. The thesis consists of three chapters. In Chapter 1 of the thesis the techniques of the stability theory which are used in Chapter 2 and Chapter 3 are overviewed. In Chapter 2 of the thesis NDFC theories are studied and the notions of dimension and U_αrank through partial orders are developed. It is proved that if the theory T is strictly stable and the the order type of rationals cannot be embedded into the fundamental order of $T$ and there is no strictly stable group interpretable in T^eq, then the theory T has continuum nonisomorphic countable models. It is noted that strongly nonisolated types can be present due to the dimensional discontinuity property. In Chapter 3 of the thesis small superstable theories are studied. In the first part of that chapter the eventualstrong and internally nonisolated types are considered, and some properties were proved. The second part of Chapter 3 contains the proof of the following theorem: if the theory T is a complete, superstable theory, the generic type of every simple group definable in T^eq is orthogonal to all NENI types and sup{U(p)pϵS(T)}≥ ω^ω holds, then the theory T has continuum nonisomorphic countable models. 