论文标题
通过扩展保存超级合理
Preservation of superamalgamation by expansions
论文作者
论文摘要
Superamalgamation属性是适用于有序结构的合并特性的强大形式。它在代数逻辑中发现了许多应用程序。我们表明，从纯模型理论的角度来看，超级合理也具有一定的兴趣。在一个完整的假设下，我们证明了某些有序结构的超级合理属性意味着对具有附加操作的类的强大合并，包括同酮，愿意，广泛，广泛，抗固定剂和封闭操作。 因此，例如，具有强大的合并属性具有强大的合并性能，例如，具有强大的合并性能（或上述操作），部分有序的集合，半层次，晶格，布尔代数和Heyting代数。与封闭操作的联接半纹身理论已完成模型。布尔代数理论（或POSET，半层次，分布晶格）具有闭合或异酮等的普遍后果是可决定的。
The superamalgamation property is a strong form of the amalgamation property which applies to ordered structures; it has found many applications in algebraic logic. We show that superamalgamation has some interest also from the pure model-theoretical point of view. Under a completion assumption, we prove that the superamalgamation property for some class of ordered structures implies strong amalgamation for classes with added operations, including isotone, idempotent, extensive, antitone and closure operations. Thus, for example, partially ordered sets, semilattices, lattices, Boolean algebras and Heyting algebras with an isotone extensive operation (or an operation as above) have the strong amalgamation property. The theory of join semilattices with a closure operation has model completion. The set of universal consequences of the theory of Boolean algebras (or posets, semilattices, distributive lattices) with a closure or isotone, etc., operation is decidable.
