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A simple presentation of the effective topos

Abstract

We propose for the Effective Topos an alternative construction: a realisability framework composed of two levels of abstraction. This construction simplifies the proof that the Effective Topos is a topos (equipped with natural numbers), which is the main issue that this paper addresses. In this our work can be compared to Frey's monadic tripos-to-topos construction. However, no topos theory or even category theory is here required for the construction of the framework itself, which provides a semantics for higher-order type theories, supporting extensional equalities and the axiom of unique choice.
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Dates and versions

hal-00844250 , version 1 (14-07-2013)

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Attribution - NonCommercial - ShareAlike

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Alexis Bernadet, Stéphane Graham-Lengrand. A simple presentation of the effective topos. [Research Report] LIX, Ecole polytechnique. 2012. ⟨hal-00844250⟩
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