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Flat Morley sequences

Published online by Cambridge University Press:  12 March 2014

Ludomir Newelski
Ludomir Newelski*
Affiliation:
Mathematical Institute of Wroclaw University, Pl.Grunwaldzki 2/4, 50–384, Wrocław, Poland E-mail: newelski@math.uni.wroc.pl Mathematical Institute of the Polish Academy of Sciences, Ul. Kopernika 18, WrocŁaw, Poland
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Abstract

Assume T is a small superstable theory. We introduce the notion of a flat Morley sequence, which is a counterpart of the notion of an infinite Morley sequence in a type p, in case when p is a complete type over a finite set of parameters. We show that for any flat Morley sequence Q there is a model M of T which is τ-atomic over {Q}. When additionally T has few countable models and is 1-based, we prove that within M there is an infinite Morley sequence I, with I ⊂ dcl(Q), such that M is prime over I.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 64 , Issue 3 , September 1999 , pp. 1261 - 1279
Copyright
Copyright © Association for Symbolic Logic 1999

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