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
收藏
页码：499 / 507
页数：9
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