Singular coverings and non‐uniform notions of closed set computability

DOI10.1002/malq.200610058zbMath1153.03043OpenAlexW2046783159MaRDI QIDQ3528149

Stéphane Le Roux, Martin Ziegler

Publication date: 8 October 2008

Published in: Mathematical Logic Quarterly (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/malq.200610058

zbMATH Keywords

connected componentco-r.e. closed setsnon-uniform computability

Mathematics Subject Classification ID

Constructive and recursive analysis (03F60) Applications of computability and recursion theory (03D80)

Related Items (9)

Computability and Analysis, a Historical Approach ⋮ The Bolzano-Weierstrass theorem is the jump of weak Kőnig's lemma ⋮ Real computation with least discrete advice: a complexity theory of nonuniform computability with applications to effective linear algebra ⋮ Semicomputable manifolds in computable topological spaces ⋮ Computational benefit of smoothness: parameterized bit-complexity of numerical operators on analytic functions and Gevrey's hierarchy ⋮ The cohesive principle and the Bolzano-Weierstraß principle ⋮ Computable neighbourhoods of points in semicomputable manifolds ⋮ Connected choice and the Brouwer fixed point theorem ⋮ Computability of Subsets of Metric Spaces

Cites Work

• Relatively recursive reals and real functions
• Computability on subsets of Euclidean space. I: Closed and compact subsets
• Computability on continuous, lower semi-continuous and upper semi-continuous real functions
• The Arithmetical Hierarchy of Real Numbers
• Effective Borel measurability and reducibility of functions
• Computable operators on regular sets
• Logical Approaches to Computational Barriers
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