François G. Dorais

Reverse mathematics and algebraic field extensions

By F. G. Dorais, J. L. Hirst and P. Shafer
Computability 2 (2013), 75–92

This paper analyzes theorems about algebraic field extensions using the techniques of reverse mathematics. In section 2, we show that $\mathsf{WKL}_0$ 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.