The Uniformity Principle for Σ-Definability with Applications to Computable Analysis.

In this paper we prove the Uniformity Principle for Σ-definability over the real numbers extended by open predicates. Using this principle we show that if we have a ΣK-formula, i.e. a formula with quantifier alternations where universal quantifiers are bounded by computable compact sets, then we can eliminate all universal quantifiers obtaining a Σ-formula equivalent to the initial one. We also illustrate how the Uniformity Principle can be employed for reasoning about computability over continuous data in an elegant way. [ABSTRACT FROM AUTHOR]