Krull dimension of types in a class of first-order theories

Authors : Domenico ZAMBELLA

Pages : 323-331

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Publication Date : 0000-00-00

Article Type : Research Paper

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 Turk J Math, vol 35, iss 2