# Applications of computability theory

#### Arno Pauly, Swansea University. Part of the Algebra, Logic, and Algorithms Seminar Series.

Computability theory is often seen as a cul-de-sac in the mathematical landscape - maybe intrinsically interesting, but without real applications in other areas of mathematics.  I will show that this is not true by showcasing two theorems (and mention several more) which are not computability-theoretic in nature, but are proven via computability-theoretic techniques.  These concern the non-existence of a universal countably-based Hausdorff topological space; and the consistent existence of an algebraically closed proper subfield of the reals with positive outer Lebesgue measure.  The former is joint work with Takayuki Kihara and Keng Meng Ng, the latter with Takayuki Kihara.

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