Louise Hay Logic Seminar
Austin Yim
Exponential Galois Theory using Model Theory
Abstract: In model theory, Galois correspondences arise in theories and their models which have a property similar to the elimination of imaginaries. The classical understanding of algebraic Galois theory can be recovered in the model-theoretic context using the appropriate and relevant theories of fields, but all theories of fields carry this requisite property. A Galois theory of exponential fields therefore exists, though not comprehensible with the model theory of complex exponentiation. The theory of psuedoexponentiation addresses some, though not all, of these difficulties, enough to characterize the algebraic subfield of the prime substructure. Using the Kronecker-Weber theorem as inspiration, some results about the abelian extensions of the prime substructure are obtained, primarily by developing a field-theoretic understanding of the algebraic subfield.
Thursday November 21, 2013 at 4:00 PM in SEO 427