An essay on model theory
Some basic ideas of model theory are presented and a personal outlook on its perspectives is given.
More on locally atomic models
A proof of Saffe's conjecture
ℳ-rank and meager types
Assume T is superstable and small. Using the multiplicity rank ℳ we find locally modular types in the same manner as U-rank considerations yield regular types. We define local versions of ℳ-rank, which also yield meager types.
ℳ-rank and meager groups
Assume p* is a meager type in a superstable theory T. We investigate definability properties of p*-closure. We prove that if T has countable models then the multiplicity rank ℳ of every type p is finite. We improve Saffe’s conjecture.
m-normal theories
Originally, m-independence, ℳ -rank, m-stability and m-normality were defined only for small stable theories. Here we extend the definitions to an arbitrary small countable complete theory. Then we investigate these notions in the new, broader context. As a consequence we show that any superstable theory with countable models is m-normal. In particular, any *-algebraic group interpretable in such a theory is abelian-by-finite.
The diameter of a Lascar strong type
We prove that a type-definable Lascar strong type has finite diameter. We also answer some other questions from [1] on Lascar strong types. We give some applications on subgroups of type-definable groups.
Weak generic types and coverings of groups I
We introduce the notion of a weak generic type in a group. We improve our earlier results on countable coverings of groups and types.
Meager forking and -independence.
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