Decidability results of subtheories of commonly used domains in Algebra and Number Theory

Abstract: We will present some known decidability and undecidability results for theories of the ring-structures of commonly used domains (Polynomial Rings, Rational Functions, Formal Power Series). Then we will focus on ongoing research relating to some subtheories such as: (a) Addition and the Frobenius map for subrings of Rational Functions of positive characteristic, and (b) Addition and Divisibility for Formal Power Series. The latter results fall mostly on the "decidability" side: model completeness and elimination of quantifiers.

commutative algebraalgebraic geometrylogicnumber theory

Audience: researchers in the topic

Online logic seminar

Series comments: Description: Seminar on all areas of logic