In chapters 2 and 3, we show, among other things that: if a theory has a strongly Ehrenfeucht model then it has arbitrarily saturated strongly Ehrenfeucht models; an unstable theory having strong Ehrenfeucht models is not multi-ordered and thus does not have the independence property; the stable theories having strongly Ehrenfeucht models are exactly the superstable theories and every saturated model of a superstable theory is strongly Ehrenfeucht. As well as using properties of indiscernible sequences, we also use some Stability Theory, various combinatorial tools and the model theory of orders - in particular dense orders without endpoints.
In chapter 4, we consider a strongly minimal theory (note that each infinite-dimensional model is a strongly Ehrenfeucht) and we study extensions of this theory in which the algebraic and definable closures coincide; such extensions are called multiplicity-1 extensions. We show that the stability spectrum of multiplicity-1 extensions is affected by the combinatorial properties of the theory: if the theory is not unimodular, its multiplicity-1 extensions are not totally transcendental; if the theory strongly eliminates imaginaries, its multiplicity-1 extensions are not stable.
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