Abstract
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.
This research was partially supported by Grant Scientific School-4413.2006.1, RFBR-DFG Project GZ: 436 RUS 113/850/01:06-01-04002 and RFBR 05-01-00819a.
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Korovina, M., Kudinov, O. (2007). The Uniformity Principle for Σ-Definability with Applications to Computable Analysis. In: Cooper, S.B., Löwe, B., Sorbi, A. (eds) Computation and Logic in the Real World. CiE 2007. Lecture Notes in Computer Science, vol 4497. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73001-9_43
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DOI: https://doi.org/10.1007/978-3-540-73001-9_43
Publisher Name: Springer, Berlin, Heidelberg
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