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Peter Schuster
University of Leeds
  1.  18
    A Constructive Look at Generalised Cauchy Reals.Peter M. Schuster - 2000 - Mathematical Logic Quarterly 46 (1):125-134.
    We investigate how nonstandard reals can be established constructively as arbitrary infinite sequences of rationals, following the classical approach due to Schmieden and Laugwitz. In particular, a total standard part map into Richman's generalised Dedekind reals is constructed without countable choice.
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  2.  30
    Countable Choice as a Questionable Uniformity Principle.Peter M. Schuster - 2004 - Philosophia Mathematica 12 (2):106-134.
    The form of nominalism known as 'mathematical fictionalism' is examined and found wanting, mainly on grounds that go back to an early antinominalist work of Rudolf Carnap that has unfortunately not been paid sufficient attention by more recent writers.
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  3.  43
    Too Simple Solutions of Hard Problems.Peter M. Schuster - 2010 - Nordic Journal of Philosophical Logic 6 (2):138-146.
    Even after yet another grand conjecture has been proved or refuted, any omniscience principle that had trivially settled this question is just as little acceptable as before. The significance of th...
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  4.  20
    Mathesis Universalis, Computability and Proof.Stefania Centrone, Sara Negri, Deniz Sarikaya & Peter M. Schuster (eds.) - 2019 - Cham, Switzerland: Springer Verlag.
    In a fragment entitled Elementa Nova Matheseos Universalis Leibniz writes “the mathesis [...] shall deliver the method through which things that are conceivable can be exactly determined”; in another fragment he takes the mathesis to be “the science of all things that are conceivable.” Leibniz considers all mathematical disciplines as branches of the mathesis and conceives the mathesis as a general science of forms applicable not only to magnitudes but to every object that exists in our imagination, i.e. that is (...)
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  5.  4
    Well-Quasi Orders in Computation, Logic, Language and Reasoning: A Unifying Concept of Proof Theory, Automata Theory, Formal Languages and Descriptive Set Theory.Peter M. Schuster, Monika Seisenberger & Andreas Weiermann (eds.) - 2020 - Cham, Switzerland: Springer Verlag.
    This book bridges the gaps between logic, mathematics and computer science by delving into the theory of well-quasi orders, also known as wqos. This highly active branch of combinatorics is deeply rooted in and between many fields of mathematics and logic, including proof theory, commutative algebra, braid groups, graph theory, analytic combinatorics, theory of relations, reverse mathematics and subrecursive hierarchies. As a unifying concept for slick finiteness or termination proofs, wqos have been rediscovered in diverse contexts, and proven to be (...)
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  6.  7
    Preface.Andrej Bauer, Thierry Coquand, Giovanni Sambin & Peter M. Schuster - 2012 - Annals of Pure and Applied Logic 163 (2):85-86.