- Turkish Journal of Mathematics
- Vol: 35 Issue: 2
- Krull dimension of types in a class of first-order theories
Krull dimension of types in a class of first-order theories
Authors : Domenico Zambella
Pages : 323-331
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Publication Date : 9999-12-31
Article Type : Makaleler
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.Keywords : Turk. J. Math., 35, (2011), 323-331. Full text: pdf Other articles published in the same issue: Turk. J. Math., vol.35, iss.2.