## Journal of Symbolic Logic

### Geometry of *-Finite Types

Ludomir Newelski

#### Abstract

Assume T is a superstable theory with $< 2^{\aleph_0}$ countable models. We prove that any *-algebraic type of $\mathscr{M}$-rank > 0 is m-nonorthogonal to a *-algebraic type of $\mathscr{M}$-rank 1. We study the geometry induced by m-dependence on a *-algebraic type p* of $\mathscr{M}$-rank 1. We prove that after some localization this geometry becomes projective over a division ring $\mathscr{F}$. Associated with p* is a meager type p. We prove that p is determined by p* up to nonorthogonality and that $\mathscr{F}$ underlies also the geometry induced by forking dependence on any stationarization of p. Also we study some *-algebraic *-groups of $\mathscr{M}$-rank 1 and prove that any *-algebraic *-group of $\mathscr{M}$-rank 1 is abelian-by-finite.

#### Article information

Source
J. Symbolic Logic, Volume 64, Issue 4 (1999), 1375-1395.

Dates
First available in Project Euclid: 6 July 2007

https://projecteuclid.org/euclid.jsl/1183745925

Mathematical Reviews number (MathSciNet)
MR1780058

Zentralblatt MATH identifier
0957.03045

JSTOR