Logics of Finite Hankel Rank

机译：有限汉克尔秩的逻辑

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We discuss the Feferman-Vaught Theorem in the setting of abstract model theory for finite structures. We look at sum-like and product-like binary operations on finite structures and their Hankel matrices. We show the connection between Hankel matrices and the Feferman-Vaught Theorem. The largest logic known to satisfy a Feferman-Vaught Theorem for product-like operations is CFOL, first order logic with modular counting quantifiers. For sum-like operations it is CMSOL, the corresponding monadic second order logic. We discuss whether there are maximal logics satisfying Feferman-Vaught Theorems for finite structures.

机译：在有限结构抽象模型理论的背景下，我们讨论了Feferman-Vaught定理。我们看一下有限结构及其Hankel矩阵上的求和式和乘积式二元运算。我们展示了汉克矩阵与费弗曼-沃特定理之间的联系。已知满足费弗曼-沃德定理的类产品运算的最大逻辑是CFOL，即带有模块化计数量词的一阶逻辑。对于类求和运算，它是CMSOL，即对应的一元二阶逻辑。我们讨论对于有限结构是否存在满足Feferman-Vaught定理的最大逻辑。

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来源
《Fields of logic and computation II: Essays Dedicated to Yuri Gurevich on the Occasion of His 75th Birthday》|2015年|237-252|共16页
会议地点 Berlin(DE)
作者
Nadia Labai; Johann A. Makowsky;
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Department of Computer Science, Technion - Israel Institute of Technology, Haifa, Israel,Department of Informatics, Vienna University of Technology, Vienna, Austria;

Department of Computer Science, Technion - Israel Institute of Technology, Haifa, Israel;

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机译：有限Hankel等级的逻辑

Logics of Finite Hankel Rank

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