论文标题
几何理论的双色扩展
Bi-Colored Expansions of Geometric Theories
论文作者
论文摘要
本文涉及根据Fraïssé-Hrushovski构造方法研究几何理论的双色扩展。几何理论$ t $的模型的子结构由颜色谓词$ p $扩展，并且与$ t $ - 代数封闭操作员的前几何相关的维数功能以及实际数字$ 0 <α\ leqslant 1 $用于定义一个预测函数$δ_α$。 The pair $(\mathcal{K}_α^{+},\leqslant_α)$ consisting of all such expansions with a hereditary positive pre-dimension along with the notion of substructure $\leqslant_α$ associated to $δ_α$ is then used as a natural setting for the study of generic bi-colored expansions in the style of Fraïssé-Hrushovski construction.在$ t $上施加某些自然条件，使我们能够为此类别中的富集结构提供完整的amotatization $ \ mathbb {t}_α$。我们将证明，如果$ t $是一个因理论（nip），那么$ \ mathbb {t}_α$也是如此。我们进一步证明，每当$α$都是合理的，强大的依赖转移到$ \ mathbb {t}_α$。我们结论说，如果$ t $定义了线性订单，而$α$是不合理的，那么$ \ mathbb {t}_α$并不强烈依赖。
This paper concerns the study of Bi-colored expansions of geometric theories in the light of the Fraïssé-Hrushovski construction method. Substructures of models of a geometric theory $T$ are expanded by a color predicate $p$, and the dimension function associated with the pre-geometry of the $T$-algebraic closure operator together with a real number $0<α\leqslant 1$ is used to define a pre-dimension function $δ_α$. The pair $(\mathcal{K}_α^{+},\leqslant_α)$ consisting of all such expansions with a hereditary positive pre-dimension along with the notion of substructure $\leqslant_α$ associated to $δ_α$ is then used as a natural setting for the study of generic bi-colored expansions in the style of Fraïssé-Hrushovski construction. Imposing certain natural conditions on $T$, enables us to introduce a complete axiomatization $\mathbb{T}_α$ for the class of rich structures in this class. We will show that if $T$ is a dependent theory (NIP) then so is $\mathbb{T}_α$. We further prove that whenever $α$ is rational the strong dependence transfers to $\mathbb{T}_α$. We conclude by showing that if $T$ defines a linear order and $α$ is irrational then $\mathbb{T}_α$ is not strongly dependent.
