  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.
