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Geometry of *-Finite Types

Ludomir Newelski
The Journal of Symbolic Logic
Vol. 64, No. 4 (Dec., 1999), pp. 1375-1395
DOI: 10.2307/2586784
Stable URL: http://www.jstor.org/stable/2586784
Page Count: 21
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Geometry of *-Finite Types
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Abstract

Assume T is a superstable theory with $< 2^{\aleph_0}$ 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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