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A simple presentation of the effective topos

By Alexis Bernadet and Stéphane Graham-lengr


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.

Topics: is simple, a topos describes an entire mathematical universe of high-order logic
Year: 2013
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