### Reverse mathematics and algebraic field extensions

##### By F. G. Dorais, J. L. Hirst and P. Shafer

###### Computability 2 (2013), 75–92

- mr: 3153994
- zbl: 1308.03038
- arxiv: 1209.4944
- doi: 10.3233/COM-13021

This paper analyzes theorems about algebraic field extensions using the techniques of reverse mathematics. In section 2, we show that is equivalent to the ability to extend -automorphisms of field extensions to automorphisms of , the algebraic closure of . 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.