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  1.  12
    Closed Choice and a Uniform Low Basis Theorem.Vasco Brattka, Matthew de Brecht & Arno Pauly - 2012 - Annals of Pure and Applied Logic 163 (8):986-1008.
  2.  5
    On the (Semi)Lattices Induced by Continuous Reducibilities.Arno Pauly - 2010 - Mathematical Logic Quarterly 56 (5):488-502.
    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.
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  3.  7
    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.
    We study the computational content of the Brouwer Fixed Point Theorem in the Weihrauch lattice. Connected choice is the operation that finds a point in a non-empty connected closed set given by negative information. One of our main results is that for any fixed dimension the Brouwer Fixed Point Theorem of that dimension is computably equivalent to connected choice of the Euclidean unit cube of the same dimension. Another main result is that connected choice is complete for dimension greater than (...)
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  4.  1
    Multi-Valued Functions in Computability Theory.Arno Pauly - 2012 - In S. Barry Cooper (ed.), How the World Computes. pp. 571--580.