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 Fˉ, 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.Comment: 25 page