Book contents
- Frontmatter
- Contents
- Introduction
- Speakers and Titles
- Thread algebra and risk assessment services
- Covering definable manifolds by open definable subsets
- Isomorphisms and definable relations on computable models
- Independence for types in algebraically closed valued fields
- Simple groups of finite Morley rank
- Towards a logic of type-free modality and truth
- Structural analysis of Aronszajn trees
- Proof analysis in non-classical logics
- Paul Bernays' later philosophy of mathematics
- Proofnets for S5: Sequents and circuits for modal logic
- Recursion on the partial continuous functionals
- A transactional approach to the logic of truth
- On some problems in computable topology
- Monotone inductive definitions and consistency of New Foundations
- LECTURE NOTES IN LOGIC
On some problems in computable topology
Published online by Cambridge University Press: 18 December 2009
- Frontmatter
- Contents
- Introduction
- Speakers and Titles
- Thread algebra and risk assessment services
- Covering definable manifolds by open definable subsets
- Isomorphisms and definable relations on computable models
- Independence for types in algebraically closed valued fields
- Simple groups of finite Morley rank
- Towards a logic of type-free modality and truth
- Structural analysis of Aronszajn trees
- Proof analysis in non-classical logics
- Paul Bernays' later philosophy of mathematics
- Proofnets for S5: Sequents and circuits for modal logic
- Recursion on the partial continuous functionals
- A transactional approach to the logic of truth
- On some problems in computable topology
- Monotone inductive definitions and consistency of New Foundations
- LECTURE NOTES IN LOGIC
Summary
Abstract. Computations in spaces like the real numbers are not done on the points of the space itself but on some representation. If one considers only computable points, i.e., points that can be approximated in a computable way, finite objects as the natural numbers can be used for this. In the case of the real numbers such an indexing can e.g. be obtained by taking the Gödel numbers of those total computable functions that enumerate a fast Cauchy sequence of rational numbers. Obviously, the numbering is only a partial map. It will be seen that this is not a consequence of a bad choice, but is so by necessity. The paper will discuss some consequences. All is done in a rather general topological framework.
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- Information
- Logic Colloquium 2005 , pp. 221 - 254Publisher: Cambridge University PressPrint publication year: 2007
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