一类一阶理论类型的克鲁尔维数
Krull dimension of types in a class of first-order theories
摘要：
我们研究一类一阶理论，其完全无量词类型与一个自由变元要么有一个平凡的正部分，或隔离的正无量词公式-加上一些其他的技术要求。向量空间理论和场理论就是例子。我们证明了合并属性和存在的模型伴侣。我们证明了模型伴侣是强极小的。我们还证明了任何素型递增序列的长度都是有界的，因此每个公式都有有限的克鲁尔维数。
英文摘要：
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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