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

ISSN: 1300-0098
Yayın Aralığı: Yılda 6 Sayı
Yayıncı: TÜBİTAK

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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