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

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

2008-12-18

arxiv.org/abs/0812.3489v2

Mathematics

Logic

Major revision, new title

Scientific paper

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.

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