Journal of Symbolic Logic

Geometry of *-Finite Types

Ludomir Newelski

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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.

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

First available in Project Euclid: 6 July 2007

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Newelski, Ludomir. Geometry of *-Finite Types. J. Symbolic Logic 64 (1999), no. 4, 1375--1395.

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