The Modified Realizability Topos

  • Jaap van Oosten

Abstract

The modified realizability topos is the semantic (and higher order) counterpart of a variant of Kreisel's modified realizability (1957). These years, this realizability has been in the limelight again because of its possibilities for modelling type theory (Streicher, Hyland-Ong-Ritter) and strong normalization.
In this paper this topos is investigated from a general logical and topostheoretic point of view. It is shown that Mod (as we call the topos) is the closed complement of the effective topos inside another one; this turns out to have some logical consequences. Some important subcategories of Mod are described, and a general logical principle is derived, which holds in the larger topos and implies the well-known Independence of Premiss principle.
Published
1996-01-03
How to Cite
Oosten, J. (1996). The Modified Realizability Topos. BRICS Report Series, 3(3). https://doi.org/10.7146/brics.v3i3.19966