214 research outputs found
Computability and analysis: the legacy of Alan Turing
We discuss the legacy of Alan Turing and his impact on computability and
analysis.Comment: 49 page
Bibliography on Realizability
AbstractThis document is a bibliography on realizability and related matters. It has been collected by Lars Birkedal based on submissions from the participants in “A Workshop on Realizability Semantics and Its Applications”, Trento, Italy, June 30–July 1, 1999. It is available in BibTEX format at the following URL: http://www.cs.cmu.edu./~birkedal/realizability-bib.html
A Convenient Category of Domains
We motivate and define a category of "topological domains",
whose objects are certain topological spaces, generalising
the usual -continuous dcppos of domain theory.
Our category supports all the standard constructions of domain theory,
including the solution of recursive domain equations. It also
supports the construction of free algebras for (in)equational
theories, provides a model of parametric polymorphism,
and can be used as the basis for a theory of computability.
This answers a question of Gordon Plotkin, who asked
whether it was possible to construct a category of domains
combining such properties
Towards a Convenient Category of Topological Domains
We propose a category of topological spaces that promises to be convenient for the purposes of domain theory as a mathematical theory for modelling computation. Our notion of convenience presupposes the usual properties of domain theory, e.g. modelling the basic type constructors, fixed points, recursive types, etc. In addition, we seek to model parametric polymorphism, and also to provide a flexible toolkit for modelling computational effects as free algebras for algebraic theories. Our convenient category is obtained as an application of recent work on the remarkable closure conditions of the category of quotients of countably-based topological spaces. Its convenience is a consequence of a connection with realizability models
Regular Functors and Relative Realizability Categories
Relative realizability toposes 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 categories that works for arbitrary base Heyting
categories. The universal property shows us some new geometric morphisms to
relative realizability toposes too
The prospects for mathematical logic in the twenty-first century
The four authors present their speculations about the future developments of
mathematical logic in the twenty-first century. The areas of recursion theory,
proof theory and logic for computer science, model theory, and set theory are
discussed independently.Comment: Association for Symbolic Logi
Mathematical Logic: Proof theory, Constructive Mathematics
The workshop “Mathematical Logic: Proof Theory, Constructive Mathematics” was centered around proof-theoretic aspects of current mathematics, constructive mathematics and logical aspects of computational complexit
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