David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
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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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References found in this work BETA
Jens Blanck (1997). Domain Representability of Metric Spaces. Annals of Pure and Applied Logic 83 (3):225-247.
V. Stoltenberg-Hansen & J. V. Tucker (1988). Complete Local Rings as Domains. Journal of Symbolic Logic 53 (2):603-624.
Citations of this work BETA
Gilda Ferreira & Paulo Oliva (2010). Confined Modified Realizability. Mathematical Logic Quarterly 56 (1):13-28.
Dieter Spreen (2010). Effectivity and Effective Continuity of Multifunctions. Journal of Symbolic Logic 75 (2):602-640.
Farzad Didehvar, Kaveh Ghasemloo & Massoud Pourmahdian (2010). Effectiveness in RPL, with Applications to Continuous Logic. Annals of Pure and Applied Logic 161 (6):789-799.
Cameron E. Freer & Daniel M. Roy (2012). Computable de Finetti Measures. Annals of Pure and Applied Logic 163 (5):530-546.
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