Affiliations: Department of Mathematics, Dartmouth College, 6188 Kemeny Hall, Hanover, NH 03755, U.S.A. [email protected], www.math.dartmouth.edu/∼dorais/ | Department of Mathematical Sciences, Appalachian State University, Boone, NC 28608, U.S.A., [email protected], mathsci2.appstate.edu/∼jlh/ | LIAFA Université Paris Diderot–Paris 7, Case 7014, 75205 Paris Cedex 13, France, [email protected], www.liafa.univ-paris-diderot.fr/∼pshafer/
Abstract: This paper analyzes theorems about algebraic field extensions using the techniques of reverse mathematics. In section §2, we show that WKL0 is equivalent to the ability to extend F-automorphisms of field extensions to automorphisms of $\bar F$, the algebraic closure of F. Section §3 explores finitary conditions for embeddability. Normal and Galois extensions are discussed in section §4, and the Galois correspondence theorems for infinite field extensions are treated in section §5.
Keywords: Reverse mathematics, algebraic field extensions, Galois theory