Berlin. - Invited lectures by Proceedings of International Congress of Mathematicians.

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Newelski, m-normal theories, preprint. Newelski, On countable meager groups, preprint. Pillay, Geometric Stability Theory, Oxford 1996. , North Holland 1990. Math. 49(1984), 259-278. D. thesis, McGill University, December 1993. pl Documenta Mathematica · Extra Volume ICM 1998 · II · 33–42 43 Doc. Math. J. DMV Basis Problems in Combinatorial Set Theory Stevo Todorcevic 1991 Mathematics Subject Classification: 04–02 An analysis of a given class S of structures in this area frequently splits into two natural parts.

Documenta Mathematica · Extra Volume ICM 1998 · II · 33–42 Meager Forking and m-Independence 35 Theorem 1 ([Ne5]) Every meager type is non-trivial and locally modular. This theorem improves [Bu1, LP]. It shows that the topological character of forking on a regular type is relevant to its geometric properties. Hrushovski and Shelah proved in [HS] that in a superstable theory without the omitting types order property (∗) every regular type is either locally modular or non-orthogonal to a strongly regular type.

We say that T has weak mcoordinatization if every ∗-algebraic type of M-rank > 0 is m-nonorthogonal to a ∗-algebraic type of M-rank 1. We say that T has full m-coordinatization if for every A and a ∗-algebraic over A with M(a/A) > 0, there is some b ∈ aclA (a) with M(b/A) = 1. The next three theorems justify our interest in m-normal theories. Theorem 7 ([Ne12]) Assume T is small, of finite M-rank. Then the following are equivalent. (1) T is m-normal. (2) T has full m-coordinatization and every ∗-algebraic M-rank 1 type is locally modular.

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