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Positive predicate structures for continuous data†

Published online by Cambridge University Press:  13 November 2014

MARGARITA KOROVINA  and
OLEG KUDINOV
MARGARITA KOROVINA
Affiliation:
A.P. Ershov Institute of Informatics systems, SB RAS, NSU, Novosibirsk, Russia Email: rita.korovina@gmail.com
OLEG KUDINOV
Affiliation:
Sobolev Institute of Mathematics, SB RAS, NSU, Novosibirsk, Russia Email: kud@math.nsc.ru
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Abstract

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In this paper, we develop a general framework for continuous data representations using positive predicate structures. We first show that basic principles of Σ-definability which are used to investigate computability, i.e., existence of a universal Σ-predicate and an algorithmic characterization of Σ-definability hold on all predicate structures without equality. Then we introduce positive predicate structures and show connections between these structures and effectively enumerable topological spaces. These links allow us to study computability over continuous data using logical and topological tools.

Footnotes

†

This research was partially supported by EU project PIRSES-GA-2011-294962, grants DFG/RFBR 1267/14-1, 14-01-91334 and RFBR 13-01-0015_a.

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