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Geometry of *-Finite Types

Published online by Cambridge University Press:  12 March 2014

Ludomir Newelski
Ludomir Newelski*
Affiliation:
Mathematical Insitute, University of Wrocław, Pl. Grunwaldzki 2/4, 50-384, Wrocław, Poland Mathematical Institute of The Polish Academy of Sciences, E-mail: newelski@math.uni.wroc.pl
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Abstract

Assume T is a superstable theory with < 2ℵ0 countable models. We prove that any *- algebraic type of -rank > 0 is m-nonorthogonal to a *-algebraic type of -rank 1. We study the geometry induced by m-dependence on a *-algebraic type p* of -rank 1. We prove that after some localization this geometry becomes projective over a division ring . Associated with p* is a meager type p. We prove that p is determined by p* up to nonorthogonality and that underlies also the geometry induced by forking dependence on any stationarization of p. Also we study some *-algebraic *-groups of -rank 1 and prove that any *-algebraic *-group of -rank 1 is abelian-by-finite.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 64 , Issue 4 , December 1999 , pp. 1375 - 1395
Copyright
Copyright © Association for Symbolic Logic 1999

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