论文标题
保存NATP
Preservation of NATP
论文作者
论文摘要
我们证明了NATP的几个保存定理，并提供了NATP的几个示例。首先，我们证明了NATP保留了fraïssé类的参数化和总和满足强融合特性的限制。其次，我们证明了NATP的两种密集/共同膨胀，即可爱对的理论以及对矢量空间上的几何理论的理论以及用于几何理论的H结构和密集/共同扩展。第三，我们证明了通用谓词扩展的NATP和一对代数封闭的场及其杰出的子场。对于后者，不仅是NATP，还考虑了NTP $ _1 $和NTP $ _2 $的保留。第四，我们使用本文证明的结果提出了一些适当的NATP示例。最重要的是，我们表明，具有循环顺序（ACFO）的代数封闭场理论的模型伴侣是NATP。
We prove several preservation theorems for NATP and furnish several examples of NATP. First, we prove preservation of NATP for the parametrization and sum of the theories of Fraïssé limits of Fraïssé classes satisfying strong amalgamation property. Second, we prove preservation of NATP for two kinds of dense/co-dense expansions, that is, the theories of lovely pairs and of H-structures for geometric theories and dense/co-dense expansion on vector spaces. Third, we prove preservation of NATP for the generic predicate expansion and the pair of an algebraically closed field and its distinguished subfield; for the latter, not only NATP, but also preservations of NTP$_1$ and NTP$_2$ are considered. Fourth, we present some proper examples of NATP using the results proved in this paper. Most of all, we show that the model companion of the theory of algebraically closed fields with circular orders (ACFO) is NATP.
