Open AccessThe Modified Realizability Topos
Author(s) -
Jaap van Oosten
Publication year - 1996
Publication title -
brics report series
Language(s) - English
Resource type - Journals
eISSN - 1601-5355
pISSN - 0909-0878
DOI - 10.7146/brics.v3i3.19966
Subject(s) - realizability , topos theory , mathematics , type theory , pure mathematics , modulo , discrete mathematics , algebra over a field , type (biology) , algorithm , art , ecology , literature , biology
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.