Vector spaces with a union of independent subspaces

被引：0

作者：

Berarducci, Alessandro ^{[1
]}

Mamino, Marcello ^{[1
]}

Mennuni, Rosario ^{[1
]}

机构：

[1] Univ Pisa, Dipartimento Matemat, Largo Bruno Pontecorvo 5, I-56127 Pisa, Italy

来源：

ARCHIVE FOR MATHEMATICAL LOGIC | 2024年 / 63卷 / 3-4期

关键词：

Model theory; Vector spaces; Independent subspaces; Stable theories; SUBGROUPS;

D O I：

10.1007/s00153-024-00906-9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：499 / 507

页数：9

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