论文标题
与独立子空间结合的向量空间
Vector spaces with a union of independent subspaces
论文作者
论文摘要
由本地定义群体理论的促进，我们研究了$ k $ - 向量空间的理论，其谓词是无限的独立子空间家族的$ x $的谓词。我们表明，如果$ k $是无限的，那么该理论是完整的，并以$ k $ - 矢量空间的语言消除了量化符，其本身为$ n $ fold $ x $的谓词。如果$ k $是有限的，这将不再正确，但是我们仍然有自然完成是近模型的。
Motivated by the theory of locally definable groups, 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.
