Reverse Mathematics and Algebraic Field Extensions

الأصل · EN

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 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.