Sheaf toposes for realizability
نویسندگان
چکیده
We compare realizability models over partial combinatory algebras by embedding them into sheaf toposes. We then use the machinery of Grothendieck toposes and geometric morphisms to study the relationship between realizability models over different partial combinatory algebras. This research is part of the Logic of Types and Computation project at Carnegie Mellon University under the direction of Dana Scott.
منابع مشابه
Tripos Theory in Retrospect
The notion of tripos (Hyland, Johnstone, and Pitts 1980; Pitts 1981) was motivated by the desire to explain in what sense Higg’s description of sheaf toposes as H-valued sets and Hyland’s realizability toposes are instances of the same construction. The construction itself can be seen as the universal solution to the problem of realizing the predicates of a first order hyperdoctrine as subobjec...
متن کاملThe Gleason Cover of a Realizability Topos
Recently Benno van den Berg [1] introduced a new class of realizability toposes which he christened Herbrand toposes. These toposes have strikingly different properties from ordinary realizability toposes, notably the (related) properties that the ‘constant object’ functor from the topos of sets preserves finite coproducts, and that De Morgan’s law is satisfied. In this paper we show that these...
متن کاملGeometric Morphisms of Realizability Toposes
We show that every geometric morphism between realizability toposes satisfies the condition that its inverse image commutes with the ‘constant object’ functors, which was assumed by John Longley in his pioneering study of such morphisms. We also provide the answer to something which was stated as an open problem on Jaap van Oosten’s book on realizability toposes: if a subtopos of a realizabilit...
متن کاملForcing for IZF in Sheaf Toposes
In [Sco] D. Scott has shown how the interpretation of intuitionistic set theory IZF in presheaf toposes can be reformulated in a more concrete fashion à la forcing as known to set theorists. In this note we show how this can be adapted to the more general case of Grothendieck toposes dealt with abstractly in [Fou, Hay].
متن کاملRegular functors and relative realisability categories
The relative realizability toposes that Awodey, Birkedal and Scott introduced in [1] satisfy a universal property that involves regular functors to other categories. We use this universal property to define what relative realizability categories are, when based on other categories than of the topos of sets. This paper explains the property and gives a construction for relative realizability cat...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Arch. Math. Log.
دوره 47 شماره
صفحات -
تاریخ انتشار 2008