Logics of Finite Hankel Rank

Chapter
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9300)

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 \(\mathrm {CFOL}\), first order logic with modular counting quantifiers. For sum-like operations it is \(\mathrm {CMSOL}\), the corresponding monadic second order logic. We discuss whether there are maximal logics satisfying Feferman-Vaught Theorems for finite structures.

Notes

Acknowledgments

We would like to thank T. Kotek for letting us use his example, and for valuable discussions.

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Department of Computer ScienceTechnion - Israel Institute of TechnologyHaifaIsrael
  2. 2.Department of InformaticsVienna University of TechnologyViennaAustria

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