Turkish Journal of Mathematics
Abstract
We study a class of first-order theories whose complete quantifier-free types with one free variable either have a trivial positive part or are isolated by a positive quantifier-free formula---plus a few other technical requirements. The theory of vector spaces and the theory fields are examples. We prove the amalgamation property and the existence of a model-companion. We show that the model-companion is strongly minimal. We also prove that the length of any increasing sequence of prime types is bounded, so every formula has finite Krull dimension.
DOI
10.3906/mat-0905-26
First Page
323
Last Page
331
Recommended Citation
ZAMBELLA, D (2011). Krull dimension of types in a class of first-order theories. Turkish Journal of Mathematics 35 (2): 323-331. https://doi.org/10.3906/mat-0905-26
