2015
DOI: 10.48550/arxiv.1511.02175
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Methods of Class Field Theory to Separate Logics over Finite Residue Classes and Circuit Complexity

Argimiro Arratia,
Carlos E. Ortiz

Abstract: Separations among the first order logic Ring(0, +, * ) of finite residue class rings, its extensions with generalized quantifiers, and in the presence of a built-in order are shown, using algebraic methods from class field theory. These methods include classification of spectra of sentences over finite residue classes as systems of congruences, and the study of their h-densities over the set of all prime numbers, for various functions h on the natural numbers. Over ordered structures the logic of finite residu… Show more

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