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From Sets and Types to Topology and Analysis: Towards Practicable Foundations for Constructive MathematicsBulletin of Symbolic Logic 12 (4): 611-612. 2006.
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34How complexity originates: Examples from history reveal additional roots to complexityComplexity 21 (S2): 7-12. 2016.
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37ContentsIn Dieter Probst & Peter Schuster (eds.), Concepts of Proof in Mathematics, Philosophy, and Computer Science, De Gruyter. 2016.
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30PrefaceIn Dieter Probst & Peter Schuster (eds.), Concepts of Proof in Mathematics, Philosophy, and Computer Science, De Gruyter. 2016.
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53Ebola-challenge and revival of theoretical epidemiology: Why Extrapolations from early phases of epidemics are problematicComplexity 20 (5): 7-12. 2015.
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44Models: From exploration to prediction: Bad reputation of modeling in some disciplines results from nebulous goalsComplexity 21 (1): 6-9. 2016.
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72Optimization of multiple criteria: Pareto efficiency and fast heuristics should be more popular than they areComplexity 18 (2): 5-7. 2013.
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124A beginning of the end of the holism versus reductionism debate?: Molecular biology goes cellular and organismicComplexity 13 (1): 10-13. 2007.
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54Boltzmann, atomism, evolution, and statistics: Continuity versus discreteness in biologyComplexity 11 (6): 9-11. 2006.
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117A revival of the landscape paradigm: Large scale data harvesting provides access to fitness landscapesComplexity 17 (5): 6-10. 2012.
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58The Kripke schema in metric topologyMathematical Logic Quarterly 58 (6): 498-501. 2012.A form of Kripke's schema turns out to be equivalent to each of the following two statements from metric topology: every open subspace of a separable metric space is separable; every open subset of a separable metric space is a countable union of open balls. Thus Kripke's schema serves as a point of reference for classifying theorems of classical mathematics within Bishop-style constructive reverse mathematics
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37A direct proof of Wiener's theoremIn S. Barry Cooper (ed.), How the World Computes, . pp. 293--302. 2012.
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83Formal Zariski topology: positivity and pointsAnnals of Pure and Applied Logic 137 (1-3): 317-359. 2006.The topic of this article is the formal topology abstracted from the Zariski spectrum of a commutative ring. After recollecting the fundamental concepts of a basic open and a covering relation, we study some candidates for positivity. In particular, we present a coinductively generated positivity relation. We further show that, constructively, the formal Zariski topology cannot have enough points
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102Quasi-apartness and neighbourhood spacesAnnals of Pure and Applied Logic 141 (1): 296-306. 2006.We extend the concept of apartness spaces to the concept of quasi-apartness spaces. We show that there is an adjunction between the category of quasi-apartness spaces and the category of neighbourhood spaces, which indicates that quasi-apartness is a more natural concept than apartness. We also show that there is an adjoint equivalence between the category of apartness spaces and the category of Grayson’s separated spaces
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104A predicative completion of a uniform spaceAnnals of Pure and Applied Logic 163 (8): 975-980. 2012.
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149A continuity principle, a version of Baire's theorem and a boundedness principleJournal of Symbolic Logic 73 (4): 1354-1360. 2008.We deal with a restricted form WC-N' of the weak continuity principle, a version BT' of Baire's theorem, and a boundedness principle BD-N. We show, in the spirit of constructive reverse mathematics, that WC-N'. BT' + ¬LPO and BD-N + ¬LPO are equivalent in a constructive system, where LPO is the limited principle of omniscience
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105Unique solutionsMathematical Logic Quarterly 52 (6): 534-539. 2006.It is folklore that if a continuous function on a complete metric space has approximate roots and in a uniform manner at most one root, then it actually has a root, which of course is uniquely determined. Also in Bishop's constructive mathematics with countable choice, the general setting of the present note, there is a simple method to validate this heuristic principle. The unique solution even becomes a continuous function in the parameters by a mild modification of the uniqueness hypothesis. …Read more
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University of LeedsRegular Faculty
Leeds, West Yorkshire, United Kingdom of Great Britain and Northern Ireland
Areas of Interest
| Logic and Philosophy of Logic |
| Medieval and Renaissance Philosophy |