This work is a step toward the development of a logic for types and computation that includes not only the usual spaces of mathematics and constructions, but also spaces from logic and domain theory. Using realizability, we investigate a configuration of three toposes that we regard as describing a notion of relative computability. Attention is focussed on a certain local map of toposes, which we first study axiomatically, and then by deriving a modal calculus as its internal logic. The resulting framework is intended as a setting for the logical and categorical study of relative computability
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
References found in this work BETA
No references found.
Citations of this work BETA
No citations found.
Similar books and articles
Sheaf Toposes for Realizability.Steven Awodey & Andrej Bauer - 2008 - Archive for Mathematical Logic 47 (5):465-478.
Relating First-Order Set Theories and Elementary Toposes.Steve Awodey, Carsten Butz & Alex Simpson - 2007 - Bulletin of Symbolic Logic 13 (3):340-358.
The Modal Logic of Stone Spaces: Diamond as Derivative.Guram Bezhanishvili, Leo Esakia & David Gabelaia - 2010 - Review of Symbolic Logic 3 (1):26-40.
Book Review: John Bell. Introduction to Toposes and Local Set Theory. [REVIEW]Colin McLarty - 1989 - Notre Dame Journal of Formal Logic 31 (1):150-161.
A Survey of Propositional Realizability Logic.Valery Plisko - 2009 - Bulletin of Symbolic Logic 15 (1):1-42.
A First Course in Logic: An Introduction to Model Theory, Proof Theory, Computability, and Complexity.Shawn Hedman - 2004 - Oxford University Press.
The Uses and Abuses of the History of Topos Theory.Colin McLarty - 1990 - British Journal for the Philosophy of Science 41 (3):351-375.
Remarks on the Development of Computability.Stewart Shapiro - 1983 - History and Philosophy of Logic 4 (1-2):203-220.
Added to index2010-09-08
Total downloads27 ( #190,306 of 2,172,870 )
Recent downloads (6 months)1 ( #324,901 of 2,172,870 )
How can I increase my downloads?