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Reverse Mathematics and Algebraic Field Extensions

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arxiv 1209.4944 v2 pith:RIH7B6X4 submitted 2012-09-22 math.LO

François G. Dorais , Jeffry Hirst , Paul Shafer This is my paper · ORCID
classification math.LO
keywords extensionsfieldsectionalgebraicautomorphismsgaloismathematicsreverse
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abstract

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.

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  1. Lifting countable to uncountable mathematics

    math.LO 2019-08 conditional novelty 4.0 of 10

    Reversals and recursive counterexamples from countable mathematics are lifted to higher-order theorems about nets, yielding principles like BOOT from monotone convergence for nets.

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