Some classes of sets of structures definable without quantifiers

J. Rogers, D. Lambert
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引用次数: 6

Abstract

We derive abstract characterizations of the Strictly Piecewise Local (SPL) and Piecewise Locally Testable (PLT) stringsets. These generalize both the Strictly Local/Locally Testable stringsets (SL and LT) and Strictly Piecewise/Piecewise Testable stringsets (SP and PT) in that SPL constraints can be stated in terms of both adjacency and precedence. We do this in a fully abstract setting which applies to any class of purely relational models that label the points in their domain with some finite labeling alphabet. This includes, for example, labeled trees and graphs. The actual structure of the class of intended models only shows up in interpreting the abstract characterizations of the definable sets in terms of the structure of the models themselves.
某些不需要量词就可以定义的结构集
给出了严格分段局部(SPL)和分段局部可测试(PLT)字符串集的抽象刻画。它们推广了严格局部/局部可测试的字符串集(SL和LT)和严格分段/分段可测试的字符串集(SP和PT),其中SPL约束可以用邻接性和优先级来表示。我们在一个完全抽象的环境中做这个,它适用于任何一类纯关系模型,这些模型用一些有限的标记字母来标记它们域内的点。这包括,例如,标记树和图。预期模型类的实际结构只有在根据模型本身的结构解释可定义集合的抽象特征时才会出现。
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