The technique of "classical realizability" is an extension of the method of
"forcing"; it permits to extend the Curry-Howard correspondence between proofs
and programs, to Zermelo-Fraenkel set theory and to build new models of ZF,
called "realizability models". The structure of these models is, in general,
much more complicated than that of the particular case of "forcing models". We
show here that the class of constructible sets of any realizability model is an
elementary extension of the constructibles of the ground model (a trivial fact
in the case of forcing, since these classes are identical). It follows that
Shoenfield absoluteness theorem applies to realizability models.Comment: 17 page
