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On Higher Effective Descriptive Set Theory

  • Margarita Korovina
  • Oleg Kudinov
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10307)

Abstract

In the framework of computable topology, we propose an approach how to develop higher effective descriptive set theory. We introduce a wide class \(\mathbb {K}\) of effective \(T_0\)-spaces admitting Borel point recovering. For this class we propose the notion of an \((\alpha ,m)\)-retractive morphism that gives a great opportunity to extend classical results from EDST to the class \(\mathbb {K}\). We illustrate this by several examples.

Keywords

Higher effective descriptive set theory Effective topological space Effective \(T_0\)–space admitting Borel point recovering \((\alpha , m)\)-retractive morphism Effective Borel and Lusin hierarchies Suslin-Kleene Theorem Uniformisation Theorem 

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.A.P. Ershov Institute of Informatics Systems, SbRASNovosibirskRussia
  2. 2.Sobolev Institute of Mathematics, SbRASNovosibirskRussia

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