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## Code-Free Recursion and Realizability

### February 24, 2014 @ 2:00 pm - 4:00 pm

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**Speaker**

Erich Faber

(University of Utrecht)

**Abstract
**The theory of partial combinatory algebras can be regarded as a generalization of both recursion theory and the theory of realizability. Partial combinatory algebras give rise to structures called realizability toposes, the archetype of which is the effective topos. The combination of the geometrical nature of a topos and the computational character of a partial combinatory algebra yields an interesting theory in which a lot is still to discover. In my talk, I will treat both sides, and discuss some results of my thesis that, for example, point out the role of generalized relative recursion in this study.