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

  • Margarita Korovina
  • Oleg Kudinov
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4497)


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 Σ K -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.


Distance Function Continuous Data Computable Analysis Free Variable Equality Test 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Margarita Korovina
    • 1
  • Oleg Kudinov
    • 2
  1. 1.Institute of Informatics Systems, pr. Lavrenteva 6, 630090, NovosibirskRussia
  2. 2.Sobolev Institute of Mathematics, pr. Koptuga 4, 630090, NovosibirskRussia

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