Filtered Order-partial Combinatory Algebras and Classical Realizability

Abstract

This thesis is mainly about classical realizability. We study a general construction of abstract Krivine structures from filtered order-partial combinatory algebras. This construction gives interesting models of classical realizability, in the sense that the corresponding Krivine toposes are not Grothendieck. From this construction, we also get a characterization of Krivine toposes among the class of realizability-related toposes. In addition, we generalize some important results about order-partial combinatory algebras to those of filtered order-partial combinatory algebras.