AN AXIOMATIC APPROACH TO FREE AMALGAMATION
AN AXIOMATIC APPROACH TO FREE AMALGAMATION
复制标题
自由合并的公理方法
DOI：
10.1017/jsl.2016.42
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
G. Conant
中科院分区：
文献类型：
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作者：
G. Conant
摘要我们用抽象三元关系公理来定义自由合并理论的概念。这些形成了一阶理论的一个子类，没有严格的顺序属性，包含了关系语言中可数结构的许多突出例子，其中代数封闭子结构的类在自由合并下是封闭的。我们证明了任何自由合并理论都有超元消去和弱超元消去。有了这个结果，我们使用几个著名的均匀结构的家庭，玫瑰色的理论给出新的例子。然后，我们证明，自由融合理论，简单性与NTP 2相一致，假设模块化，与NSOP 3以及。我们还表明，任何简单的自由融合理论是1-基。最后，我们证明了自由合并Fraïssé极限的简单性的一个组合刻画，这为一般的无Kn-图是SOP 3，而更高元数的无$Kn ^r$-超图是简单的这一事实提供了新的背景.
Abstract We use axioms of abstract ternary relations to define the notion of a free amalgamation theory. These form a subclass of first-order theories, without the strict order property, encompassing many prominent examples of countable structures in relational languages, in which the class of algebraically closed substructures is closed under free amalgamation. We show that any free amalgamation theory has elimination of hyperimaginaries and weak elimination of imaginaries. With this result, we use several families of well-known homogeneous structures to give new examples of rosy theories. We then prove that, for free amalgamation theories, simplicity coincides with NTP2 and, assuming modularity, with NSOP3 as well. We also show that any simple free amalgamation theory is 1-based. Finally, we prove a combinatorial characterization of simplicity for Fraïssé limits with free amalgamation, which provides new context for the fact that the generic K n -free graphs are SOP3, while the higher arity generic $K_n^r$ -free r-hypergraphs are simple.
一些 Hrushovski 构造的自同构群的简性
DOI：
10.1016/j.apal.2015.09.002
发表时间：
2016
期刊：
Ann. Pure Appl. Log.
影响因子：
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作者：
David M. Evans;Zaniar Ghadernezhad;Katrin Tent
通讯作者：
Katrin Tent