The Classification of Small Types of Rank $\omega$, Part I
Buechler, Steven ; Hoover, Colleen
J. Symbolic Logic, Tome 66 (2001) no. 1, p. 1884-1898 / Harvested from Project Euclid
Certain basic concepts of geometrical stability theory are generalized to a class of closure operators containing algebraic closure. A specific case of a generalized closure operator is developed which is relevant to Vaught's conjecture. As an application of the methods, we prove THEOREM A. Let G be a superstable group of U-rank $\omega$ such that the generics of G are locally modular and Th(G) has few countable models. Let $G^-$ be the group of nongeneric elements of G, G$^+$ = G$^o$ + G$^-$. Let $\Pi$= $\{$q $\in$ S($\emptyset$): U(q) < $\omega\}$. For any countable model M of Th(G) there is a finite $A \subset M$ such that M is almost atomic over $A \cup$ (G$^+$ $\cap$ M) $\cup \bigcup_{p\in \Pi}$p(M).
Publié le : 2001-12-14
Classification: 
@article{1183746632,
     author = {Buechler, Steven and Hoover, Colleen},
     title = {The Classification of Small Types of Rank $\omega$, Part I},
     journal = {J. Symbolic Logic},
     volume = {66},
     number = {1},
     year = {2001},
     pages = { 1884-1898},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1183746632}
}
Buechler, Steven; Hoover, Colleen. The Classification of Small Types of Rank $\omega$, Part I. J. Symbolic Logic, Tome 66 (2001) no. 1, pp.  1884-1898. http://gdmltest.u-ga.fr/item/1183746632/