- New
-
Topics
- All Categories
- Metaphysics and Epistemology
- Value Theory
- Science, Logic, and Mathematics
- Science, Logic, and Mathematics
- Logic and Philosophy of Logic
- Philosophy of Biology
- Philosophy of Cognitive Science
- Philosophy of Computing and Information
- Philosophy of Mathematics
- Philosophy of Physical Science
- Philosophy of Social Science
- Philosophy of Probability
- General Philosophy of Science
- Philosophy of Science, Misc
- History of Western Philosophy
- Philosophical Traditions
- Philosophy, Misc
- Other Academic Areas
- Journals
- Submit material
- More
Singular coverings and non‐uniform notions of closed set computability
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 pointMy notes
Similar books and articles
Ultrafilters generated by a closed set of functions.Greg Bishop - 1995 - Journal of Symbolic Logic 60 (2):415-430.
Uniform domain representations of "Lp" -spaces.Petter K. Køber - 2007 - Mathematical Logic Quarterly 53 (2):180-205.
Random closed sets viewed as random recursions.R. Daniel Mauldin & Alexander P. McLinden - 2009 - Archive for Mathematical Logic 48 (3-4):257-263.
Uniform unfolding and analytic measurability.Benedikt Löwe - 1998 - Archive for Mathematical Logic 37 (8):505-520.
Reverse mathematics of separably closed sets.Jeffry L. Hirst - 2006 - Archive for Mathematical Logic 45 (1):1-2.
A characterization of the $\Sigma_1$ -definable functions of $KP\omega + $.Wolfgang Burr & Volker Hartung - 1998 - Archive for Mathematical Logic 37 (3):199-214.
On the notion of effectiveness.Stewart Shapiro - 1980 - History and Philosophy of Logic 1 (1-2):209-230.
Constructive complements of unions of two closed sets.Douglas S. Bridges - 2004 - Mathematical Logic Quarterly 50 (3):293.
Computability on Regular Subsets of Euclidean Space.Martin Ziegler - 2002 - Mathematical Logic Quarterly 48 (S1):157-181.
Strong Computability and Variants of the Uniform Halting Problem.Gabor T. Herman - 1971 - Mathematical Logic Quarterly 17 (1):115-131.
Computability of measurable sets via effective topologies.Yongcheng Wu & Decheng Ding - 2006 - Archive for Mathematical Logic 45 (3):365-379.
Order-Computable Sets.Denis Hirschfeldt, Russell Miller & Sergei Podzorov - 2007 - Notre Dame Journal of Formal Logic 48 (3):317-347.
Computability and continuity in computable metric partial algebras equipped with computability structures.Fredrik Dahlgren - 2004 - Mathematical Logic Quarterly 50 (4):486.
Computability of Self‐Similar Sets.Hiroyasu Kamo & Kiko Kawamura - 1999 - Mathematical Logic Quarterly 45 (1):23-30.
On closed p-sets with $\operatorname{ccc}$ in the ω.Rvszard Frankiewicz, Saharon Shelah & Pawel Zbierski - 1993 - Journal of Symbolic Logic 58 (4):1171 - 1176.
Analytics
Added to PP
2013-12-01
Downloads
28 (#536,385)
6 months
2 (#1,136,865)
2013-12-01
Downloads
28 (#536,385)
6 months
2 (#1,136,865)
Historical graph of downloads
Citations of this work
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.
References found in this work
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 (4-5):392-404.
PhilPapers logo by Andrea Andrews and Meghan Driscoll.
This site uses cookies and Google Analytics (see our terms & conditions for details regarding the privacy implications). Use of this site is subject to terms & conditions.
All rights reserved by The PhilPapers Foundation
Server: philpapers-web-6d9b7f7c4c-67rzb uwo