Logics of Finite Hankel Rank
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.
Cite
@article{arxiv.1512.02507,
title = {Logics of Finite Hankel Rank},
author = {Nadia Labai and Johann A. Makowsky},
journal= {arXiv preprint arXiv:1512.02507},
year = {2015}
}
Comments
Appeared in YuriFest 2015, held in honor of Yuri Gurevich's 75th birthday. The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-319-23534-9_14