Geometry of *-finite types

Journal of Symbolic Logic 64 (4):1375-1395 (1999)
Abstract
Assume T is a superstable theory with $ countable models. We prove that any *-algebraic type of M-rank > 0 is m-nonorthogonal to a *-algebraic type of M-rank 1. We study the geometry induced by m-dependence on a *-algebraic type p* of M-rank 1. We prove that after some localization this geometry becomes projective over a division ring F. Associated with p* is a meager type p. We prove that p is determined by p* up to nonorthogonality and that F underlies also the geometry induced by forking dependence on any stationarization of p. Also we study some *-algebraic *-groups of M-rank 1 and prove that any *-algebraic *-group of M-rank 1 is abelian-by-finite
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DOI 10.2307/2586784
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References found in this work BETA
Meager Forking.Ludomir Newelski - 1994 - Annals of Pure and Applied Logic 70 (2):141-175.
Locally Modular Theories of Finite Rank.Steven Buechler - 1986 - Annals of Pure and Applied Logic 30 (1):83-94.
On Type Definable Subgroups of a Stable Group.L. Newelski - 1991 - Notre Dame Journal of Formal Logic 32 (2):173-187.
Weakly Minimal Formulas: A Global Approach.Ludomir Newelski - 1990 - Annals of Pure and Applied Logic 46 (1):65-94.

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