ℳ-rank and meager groups

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Institute of Mathematics, Polish Academy of Sciences, Wrocław Branch, Kopernika 18, 51-617 Wrocław, Poland

Assume p* is a meager type in a superstable theory T. We investigate definability properties of p*-closure. We prove that if T has

< 2^{ℵ_{0}}

countable models then the multiplicity rank ℳ of every type p is finite. We improve Saffe's conjecture.

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