Positive predicate structures for continuous data

摘要

In this paper, we develop a general framework for continuous data representations using positive predicate structures. We first show that basic principles of Sigma-definability which are used to investigate computability, i.e., existence of a universal Sigma-predicate and an algorithmic characterization of Sigma-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.