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arXiv 2011.040342020-11math.LO

一个具有非代数几何闭包的驯服一般结构

A Tame Generic Structure with Non-Algebraic Geometric Closure

Somaye Jalili, Massoud Pourmahdian, Ali N. Valizadeh

备注：: In this version we prove that the decidable theory of paracollapsed structures has SOP and TP_2. Moreover, we bring examples of formulas witnessing SOP_3, and SOP_n for all n greater than or equal to 2

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AI总结：

本文引入paracollapsed结构，通过Hrushovski合并方法构造存在闭的一般结构，其几何闭包不包含于代数闭包且理论可判定，并证明该结构具有严格序性质和TP2。

摘要：

通过提供一种将Hrushovski的合并方法应用于无限结构类设置的程序，我们引入了\textit{paracollapsed}结构的概念。我们证明这种方法提供了存在闭的一般结构，其中几何闭包不包含在代数闭包中，而所得理论是可判定的。我们证明paracollapsed结构具有严格序性质和$\text{TP}_2$。

英文摘要：

By providing a procedure to apply Hrushovski's amalgamation method to the setting of classes of infinite structures, we introduce the notion of \textit{paracollapsed} structures. We show that this approach provides existentially closed generic structures in which the geometric closure is not included in the algebraic closure while the resulting theory is decidable. We show that paracollapsed structures have the strict order property and $\text{TP}_2$.

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