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We characterize nonforking (Morley) sequences in dependent theories in terms of a generalization of Poizats special sequences and show that average types of Morley sequences are stationary over their domains. We characterize generically stable types in terms of the structure of the eventual type. We then study basic properties of strict Morley sequences, based on Shelahs notion of strict nonforking. In particular we prove Kims lemma for such sequences, and a weak version of local character.
We develop the theory of generically stable types, independence relation based on nonforking and stable weight in the context of dependent (NIP) theories.
By exploiting the geometry of involutions in $N_circ^circ$-groups of finite Morley rank, we show that any simple group of Morley rank $5$ is a bad group all of whose proper definable connected subgroups are nilpotent of rank at most $2$. The main res
The present survey aims at being a list of Conjectures and Problems in an area of model-theoretic algebra wide open for research, not a list of known results. To keep the text compact, it focuses on structures of finite Morley rank, although the same
We show that a locally finite Borel graph is nonsmooth if and only if it admits marker sequences which are far from every point. Our proof uses the Galvin-Prikry theorem and the Glimm-Effros dichotomy.
We give examples of (i) a simple theory with a formula (with parameters) which does not fork over the empty set but has mu measure 0 for every automorphism invariant Keisler measure mu, and (ii) a definable group G in a simple theory such that G is n