Fields with a dense-codense linearly independent multiplicative subgroup
Fields with a dense-codense linearly independent multiplicative subgroup
复制标题
具有稠密线性无关乘法子群的域
DOI：
--
复制
发表时间：
2020
影响因子：
0.3
通讯作者：
E. Vassiliev
中科院分区：
文献类型：
--
作者：
A. Berenstein;E. Vassiliev
研究了代数闭域K或实闭域R与其乘子群G的线性无关子群或单位圆群$${mathbb{S}}(R)$$S(R)的展开，满足密度/余密度条件(在几何理论意义下).由于集合G既不是代数封闭的，也不是代数独立的，这种展开式可以看作是几何理论的另外两种密集/凝聚展开式的“中间”：可爱对和H-结构。我们证明了在代数闭域和实闭域两种情况下，所得到的理论都是接近模型完全的，并且展开式保持了许多与可定义集的复杂性有关的良好的模型理论条件，如稳定性和NIP。
We study expansions of an algebraically closed field K or a real closed field R with a linearly independent subgroup G of the multiplicative group of the field or the unit circle group $${mathbb {S}}(R)$$ S ( R ) , satisfying a density/codensity condition (in the sense of geometric theories). Since the set G is neither algebraically closed nor algebraically independent, the expansion can be viewed as “intermediate” between the two other types of dense/codense expansions of geometric theories: lovely pairs and H -structures. We show that in both the algebraically closed field and real closed field cases, the resulting theory is near model complete and the expansion preserves many nice model theoretic conditions related to the complexity of definable sets such as stability and NIP.