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arXiv · 1512.02507

Logics of Finite Hankel Rank

Nadia Labai·Johann A. Makowsky
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Abstract

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.

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Nadia Labai, Johann A. Makowsky. 2015-12-08. Logics of Finite Hankel Rank. https://doi.org/10.1007/978-3-319-23534-9_14

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