Mathematical Logic Quarterly 54 (5):545-560 (2008)
| Abstract |
The empty set of course contains no computable point. On the other hand, surprising results due to Zaslavskiĭ, Tseĭtin, Kreisel, and Lacombe have asserted the existence of non-empty co-r. e. closed sets devoid of computable points: sets which are even “large” in the sense of positive Lebesgue measure.This leads us to investigate for various classes of computable real subsets whether they always contain a computable point
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| Keywords | Co‐r. e. closed sets connected component non‐uniform computability |
| Categories | (categorize this paper) |
| DOI | 10.1002/malq.200610058 |
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References found in this work BETA
Effective Borel Measurability and Reducibility of Functions.Vasco Brattka - 2005 - Mathematical Logic Quarterly 51 (1):19-44.
The Arithmetical Hierarchy of Real Numbers.Xizhong Zheng & Klaus Weihrauch - 2001 - Mathematical Logic Quarterly 47 (1):51-66.
Ensembles Récursivement Mesurable Et Ensembles Récursivement Ouverts Ou Fermés.Georg Kreisel & Daniel Lacombe - 1966 - Journal of Symbolic Logic 31 (1):133-133.
Computable Operators on Regular Sets.Martin Ziegler - 2004 - Mathematical Logic Quarterly 50 (45):392-404.
Citations of this work BETA
The Bolzano–Weierstrass Theorem is the Jump of Weak Kőnig’s Lemma.Vasco Brattka, Guido Gherardi & Alberto Marcone - 2012 - Annals of Pure and Applied Logic 163 (6):623-655.
Computable Neighbourhoods of Points in Semicomputable Manifolds.Zvonko Iljazović & Lucija Validžić - 2017 - Annals of Pure and Applied Logic 168 (4):840-859.
The Cohesive Principle and the Bolzano‐Weierstraß Principle.Alexander P. Kreuzer - 2011 - Mathematical Logic Quarterly 57 (3):292-298.
Connected Choice and the Brouwer Fixed Point Theorem.Vasco Brattka, Stéphane Le Roux, Joseph S. Miller & Arno Pauly - 2019 - Journal of Mathematical Logic 19 (1):1950004.
Real Computation with Least Discrete Advice: A Complexity Theory of Nonuniform Computability with Applications to Effective Linear Algebra.Martin Ziegler - 2012 - Annals of Pure and Applied Logic 163 (8):1108-1139.
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