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.

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Publié le : 1987-12-14
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