# Realizability with truth for arbitrary partial combinatory algebras

#### Eman Dihoum, University of Leeds. Part of the proofs, constructions and computations seminar series.

The main part of the talk consists of defining realizability with truth for an arbitrary applicative, V^*(\mathcal A). This notion of realizability was introduced in a paper by Rathjen. Rathjen showed that CZF and CZF+REA are sound for the special case of V^*(K_{1}), where K_{1} is Kleene\'s first model and we also establish similar results when moving from V^*(K_{1}) to V^*(\mathcal A) for any applicative structure \mathcal A. In the end I will just mention a few metamathematical results about CZF that can be obtained using this technique.

Eman DihoumUniversity of Leeds

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