Geometry of *-Finite Types
Newelski, Ludomir
J. Symbolic Logic, Tome 64 (1999) no. 1, p. 1375-1395 / Harvested from Project Euclid
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.
Publié le : 1999-12-14
Classification: 
@article{1183745925,
     author = {Newelski, Ludomir},
     title = {Geometry of *-Finite Types},
     journal = {J. Symbolic Logic},
     volume = {64},
     number = {1},
     year = {1999},
     pages = { 1375-1395},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1183745925}
}
Newelski, Ludomir. Geometry of *-Finite Types. J. Symbolic Logic, Tome 64 (1999) no. 1, pp.  1375-1395. http://gdmltest.u-ga.fr/item/1183745925/