具有独立子空间联合的向量空间

IF 0.4 4区数学 Q4 LOGIC

Archive for Mathematical Logic Pub Date : 2024-02-17 DOI:10.1007/s00153-024-00906-9

Alessandro Berarducci, Marcello Mamino, Rosario Mennuni

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引用次数: 0

摘要

我们研究了 K 向量空间的理论，其中有一个谓词是独立子空间无穷族的联合 X。我们证明，如果 K 是无限的，那么这个理论就是完备的，并且可以用 K 向量空间的语言用 X 与自身的 n 次和的谓词进行量词消元。如果 K 是有限的，这一点就不再成立，但我们仍然认为自然完备性接近于模型完备性。

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Vector spaces with a union of independent subspaces

We study the theory of K-vector spaces with a predicate for the union X of an infinite family of independent subspaces. We show that if K is infinite then the theory is complete and admits quantifier elimination in the language of K-vector spaces with predicates for the n-fold sums of X with itself. If K is finite this is no longer true, but we still have that a natural completion is near-model-complete.

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来源期刊

Archive for Mathematical Logic 数学-数学

自引率

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发文量

期刊介绍： The journal publishes research papers and occasionally surveys or expositions on mathematical logic. Contributions are also welcomed from other related areas, such as theoretical computer science or philosophy, as long as the methods of mathematical logic play a significant role. The journal therefore addresses logicians and mathematicians, computer scientists, and philosophers who are interested in the applications of mathematical logic in their own field, as well as its interactions with other areas of research.