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Effective metric model theory


This paper is a further investigation of a project carried out in Didehvar and Ghasemloo (2009) to study effective aspects of the metric logic. We prove an effective version of the omitting types theorem. We also present some concrete computable constructions showing that both the separable atomless probability algebra and the rational Urysohn space are computable metric structures.

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I. Ben Yaacov and A. Usvyatsov (2007) On d-finiteness in continous structures. Fundamenta Mathematicae 194 6788.

C. C. Chang and H. J. Keisler (1966) Continuous Model Theory, Princeton University Press.

T. Grubba , K. Weihrauch and Y. Xu (2008) Effectivity on continuous functions in topological spaces. In: R. Dillhage , T. Grubba , A. Sorbi , K. Weihrauch and N. Zhong (eds.) Proceedings of the Fourth International Conference on Computability and Complexity in Analysis (CCA 2007). Electronic Notes in Theoretical Computer Science 202 3–12. (Elsevier. CCA 2007, Siena, Italy, June 16–18, 2007.)

W. Hodges (1993) Model Theory, Cambridge University Press.

A. Usvyatsov (2008) Generic separable metric structures. Topology and its Applications 155 16071617.

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Mathematical Structures in Computer Science
  • ISSN: 0960-1295
  • EISSN: 1469-8072
  • URL: /core/journals/mathematical-structures-in-computer-science
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