On Two Hierarchies of Dimensions

Baudisch, Andreas

J. Symbolic Logic, Tome 52 (1987) no. 1, p. 959-968 / Harvested from Project Euclid

Résumé

Let $T$ be a countable, complete, $\omega$-stable, nonmultidimensional theory. By Lascar [7], in $T^{\mathrm{eq}}$ there is in every dimension of $T$ a type with Lascar rank $\omega^\alpha$ for some $\alpha$. We give sufficient conditions for $\alpha$ to coincide with the level of that dimension in Pillay's [10] RK-hierarchy of dimensions computed in $T^{\mathrm{eq}}$. In particular, this is fulfilled for modules.

Publié le : 1987-12-14
Classification:

@article{1183742505,
     author = {Baudisch, Andreas},
     title = {On Two Hierarchies of Dimensions},
     journal = {J. Symbolic Logic},
     volume = {52},
     number = {1},
     year = {1987},
     pages = { 959-968},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1183742505}
}

Baudisch, Andreas. On Two Hierarchies of Dimensions. J. Symbolic Logic, Tome 52 (1987) no. 1, pp.  959-968. http://gdmltest.u-ga.fr/item/1183742505/