DECOMPOSITION THEOREM AND APPLICATIONS RAMI GROSSBERG AND OLIVIER LESSMANN Abstract. In this paper, we prove a decomposition theorem for abstract elementary classes K with the amalgamation property, under the assumption that certain axioms regarding independence, existence of some prime models, and regular types are satisfied. This context encompasses the following: (1) K is the class of models...

We give an example of an infinite simple Frobenius group G without involutions, with a trivial kernel and a nilpotent complement. Nevertheless, this group is not ωstable (not even superstable), this is the ”only” property missing in order to be a counterexample to the Cherlin-Zil’ber Conjecture which says that simple ωstable groups are algebraic groups.

The aim of this paper is to analyze different regulation mechanisms in spatial continuous stochastic development models. We describe the density behavior for models with global mortality and local establishment rates. We prove that the local self-regulation via a competition mechanism (density dependent mortality) may suppress a unbounded growth of the averaged density if the competition kernel...

We prove that the generic type of the (theory of the) free group Fn on n ≥ 2 generators has infinite weight, strengthening the well-known result that these free groups are not superstable. A preliminary result, possibly of independent interest, is that the realizations in Fn of the generic type are precisely the primitives.

We prove that IHSA, the theory of infinite dimensional Hilbert spaces equipped with a generic automorphism, is א0-stable up to perturbation of the automorphism, and admits prime models up to perturbation over any set. Similarly, APrA, the theory of atomless probability algebras equipped with a generic automorphism is א0-stable up to perturbation. However, not allowing perturbation it is not eve...

In Bue93b] we proved Vaught's conjecture for all superstable theories of nite rank; that is, such a theory has countably many or continuum many countable models. While this proof does settle Vaught's conjecture for unidimensional theories a sharper result can be obtained for these theories and in places the proof can be simpliied. Let T be a properly unidimensional theory with < 2 @ 0 many coun...