Uniformity principle for $\Sigma$-definability

Margarita, Korovina and Oleg, Kudinov (2009) Uniformity principle for $\Sigma$-definability. Journal of Logic and Computation, 19 (1). pp. 159-174. ISSN 0955-792X

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Abstract

The main goal of this research is to develop logical tools and techniques for effective reasoning about continuous data based on $\Sigma$-definability. In this article we invent the Uniformity Principleand prove it for $\Sigma$-definability over the real numbers extended by open predicates. Using the Uniformity Principle, we investigate different approaches to enrich the language of {Sigma}-formulas in such a way that simplifies reasoning about computable continuous data without enlarging the class of $\Sigma$-definable sets. In order to do reasoning about computability of certain continuous data we have to pick up an appropriate language of a structure representing these continuous data. We formulate several major conditions how to do that in a right direction. We also employ the Uniformity Principleto argue that our logical approach is a good way for formalization of computable continuous data in logical terms.

Item Type:	Article
Uncontrolled Keywords:	CICADA,$\Sigma$-Definability, Uniformity Principle, effective reasoning about continuous data, continuous data types, computable analysis
Subjects:	MSC 2010, the AMS's Mathematics Subject Classification > 03 Mathematical logic and foundations MSC 2010, the AMS's Mathematics Subject Classification > 68 Computer science
Depositing User:	Dr Margarita Korovina
Date Deposited:	08 Jan 2010
Last Modified:	20 Oct 2017 14:12
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/1377

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