Positive predicate structures for continuous data

Abstract

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.