Domains for computation in mathematics, physics and exact real arithmetic

Bulletin of Symbolic Logic 3 (4):401-452 (1997)
We present a survey of the recent applications of continuous domains for providing simple computational models for classical spaces in mathematics including the real line, countably based locally compact spaces, complete separable metric spaces, separable Banach spaces and spaces of probability distributions. It is shown how these models have a logical and effective presentation and how they are used to give a computational framework in several areas in mathematics and physics. These include fractal geometry, where new results on existence and uniqueness of attractors and invariant distributions have been obtained, measure and integration theory, where a generalization of the Riemann theory of integration has been developed, and real arithmetic, where a feasible setting for exact computer arithmetic has been formulated. We give a number of algorithms for computation in the theory of iterated function systems with applications in statistical physics and in period doubling route to chaos; we also show how efficient algorithms have been obtained for computing elementary functions in exact real arithmetic
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DOI 10.2307/421098
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References found in this work BETA
Domain Representability of Metric Spaces.Jens Blanck - 1997 - Annals of Pure and Applied Logic 83 (3):225-247.
Complete Local Rings as Domains.V. Stoltenberg-Hansen & J. V. Tucker - 1988 - Journal of Symbolic Logic 53 (2):603-624.

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Confined Modified Realizability.Gilda Ferreira & Paulo Oliva - 2010 - Mathematical Logic Quarterly 56 (1):13-28.
Effectivity and Effective Continuity of Multifunctions.Dieter Spreen - 2010 - Journal of Symbolic Logic 75 (2):602-640.
Computable de Finetti Measures.Cameron E. Freer & Daniel M. Roy - 2012 - Annals of Pure and Applied Logic 163 (5):530-546.

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