On the (semi)lattices induced by continuous reducibilities

Abstract

Continuous reducibilities are a proven tool in computable analysis, and have applications in other fields such as constructive mathematics or reverse mathematics. We study the order-theoretic properties of several variants of the two most important definitions, and especially introduce suprema for them. The suprema are shown to commutate with several characteristic numbers.

this version of the paper is outdated, please consult the journal version

Cited by in corpus (15)

• Closed Choice and a Uniform Low Basis Theorem
• The Bolzano-Weierstrass Theorem is the Jump of Weak König's Lemma
• Effective Choice and Boundedness Principles in Computable Analysis
• Computability and analysis: the legacy of Alan Turing
• Probabilistic Computability and Choice
• Non-deterministic computation and the Jayne-Rogers Theorem
• On the Uniform Computational Content of Computability Theory
• On the existence of a connected component of a graph
• Weihrauch goes Brouwerian
• Many-one reductions and the category of multivalued functions
• On the Uniform Computational Content of the Baire Category Theorem
• The Discontinuity Problem
• Computability and Analysis, a Historical Approach
• The Vitali Covering Theorem in the Weihrauch Lattice
• Projection operators in the Weihrauch lattice