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Peter Schuster [58]Peter M. Schuster [3]Peters Schuster [1]
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Profile: Peter Schuster (University of Leeds)
  1. Peter Aczel, Benno van den Berg, Johan Granström & Peter Schuster (forthcoming). Are There Enough Injective Sets? Studia Logica.
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  2. Riccardo Bruni & Peter Schuster (forthcoming). Approximating Beppo Levi's "Principio di Approssimazione". Association for Symbolic Logic: The Bulletin of Symbolic Logic.
    We try to recast in modern terms a choice principle conceived by Beppo Levi. who called it the Approximation Principle (AP). Up to now. there was almost no discussion about Levi's contribution. due to the quite obscure formulation of AP the author has chosen. After briefly reviewing the historical and philosophical surroundings of Levi's proposal. we undertake our own attempt at interpreting AP. The idea underlying the principle. as well as the supposed faithfulness of our version to Levi's original intention. (...)
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  3. Peter Schuster (forthcoming). How Do RNA Molecules and Viruses Explore Their Worlds? Complexity.
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  4. Peter Schuster (2014). Are Computer Scientists the Sutlers of Modern Biology?: Bioinformatics is Indispensible for Progress in Molecular Life Sciences but Does Not Get Credit for its Contributions. Complexity 19 (4):10-14.
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  5. Peter Aczel, Benno Berg, Johan Granström & Peter Schuster (2013). Are There Enough Injective Sets? Studia Logica 101 (3):467-482.
    The axiom of choice ensures precisely that, in ZFC, every set is projective: that is, a projective object in the category of sets. In constructive ZF (CZF) the existence of enough projective sets has been discussed as an additional axiom taken from the interpretation of CZF in Martin-Löf’s intuitionistic type theory. On the other hand, every non-empty set is injective in classical ZF, which argument fails to work in CZF. The aim of this paper is to shed some light on (...)
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  6. Peter Schuster (2013). A Silent Revolution in Mathematics. Complexity 18 (6):7-10.
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  7. Peter Schuster (2013). Designing Living Matter. Can We Do Better Than Evolution? Complexity 18 (6):21-33.
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  8. Peter Schuster (2013). Recycling and Growth in Early Evolution and Today. Complexity 19 (2):6-9.
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  9. Andrej Bauer, Thierry Coquand, Giovanni Sambin & Peter M. Schuster (2012). Preface. Annals of Pure and Applied Logic 163 (2):85-86.
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  10. Josef Berger, Hajime Ishihara, Erik Palmgren & Peter Schuster (2012). A Predicative Completion of a Uniform Space. Annals of Pure and Applied Logic 163 (8):975-980.
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  11. Matthew Hendtlass & Peter Schuster (2012). A Direct Proof of Wiener's Theorem. In S. Barry Cooper (ed.), How the World Computes. 293--302.
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  12. Robert S. Lubarsky, Fred Richman & Peter Schuster (2012). The Kripke Schema in Metric Topology. Mathematical Logic Quarterly 58 (6):498-501.
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  13. Peter Schuster (2012). A Revival of the Landscape Paradigm: Large Scale Data Harvesting Provides Access to Fitness Landscapes. Complexity 17 (5):6-10.
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  14. Peter Schuster (2012). Optimization of Multiple Criteria: Pareto Efficiency and Fast Heuristics Should Be More Popular Than They Are. Complexity 18 (2):5-7.
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  15. Hajime Ishihara & Peter Schuster (2011). On the Contrapositive of Countable Choice. Archive for Mathematical Logic 50 (1-2):137-143.
    We show that in elementary analysis (EL) the contrapositive of countable choice is equivalent to double negation elimination for ${\Sigma_{2}^{0}}$ -formulas. By also proving a recursive adaptation of this equivalence in Heyting arithmetic (HA), we give an instance of the conservativity of EL over HA with respect to recursive functions and predicates. As a complement, we prove in HA enriched with the (extended) Church thesis that every decidable predicate is recursive.
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  16. Peter Schuster (2011). Is There a Newton of the Blade of Grass? Complexity 16 (6):5-9.
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  17. Peter Schuster (2011). Lethal Mutagenesis, Error Thresholds, and the Fight Against Viruses: Rigorous Modeling is Facilitated by a Firm Physical Background. Complexity 17 (2):5-9.
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  18. Peter Schuster (2011). Networks in Biology: Handling Biological Complexity Requires Novel Inputs Into Network Theory. Complexity 16 (4):6-9.
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  19. Peter Schuster (2011). Power Laws in Biology: Between Fundamental Regularities and Useful Interpolation Rules. Complexity 16 (3):6-9.
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  20. Peter Schuster (2010). Contingeny and Memory in Evolution. Complexity 15 (6):7-10.
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  21. Peter Schuster (2010). Origins of Life: Concepts, Data, and Debates. Complexity 15 (3):7-10.
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  22. Peter Schuster (2010). Power Laws in Biology. Complexity 16:6-9.
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  23. Peter Schuster (2009). Free Will, Information, Quantum Mechanics, and Biology. Complexity 15 (1):8-10.
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  24. Josef Berger, Dirk Pattinson, Peter Schuster & Júlia Zappe (2008). Editorial: Math. Log. Quart. 1/2008. Mathematical Logic Quarterly 54 (1):4-4.
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  25. Hajime Ishihara & Peter Schuster (2008). A Continuity Principle, a Version of Baire's Theorem and a Boundedness Principle. Journal of Symbolic Logic 73 (4):1354-1360.
    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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  26. Peter Schuster (2008). Are There Recipes for How to Handle Complexity? Complexity 14 (1):8-12.
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  27. Peter Schuster (2008). Editorial Remarks. Complexity 13 (6):11-11.
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  28. Peters Schuster & Julia Zappe (2008). About Kripke's Schema and Countable Subsets. Logique Et Analyse 204:317-329.
     
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  29. Peter Schuster (2007). A Beginning of the End of the Holism Versus Reductionism Debate?: Molecular Biology Goes Cellular and Organismic. Complexity 13 (1):10-13.
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  30. Peter Schuster (2007). Corrigendum to “Unique Solutions”. Mathematical Logic Quarterly 53 (2):214-214.
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  31. Peter Schuster (2007). Nonlinear Dynamics From Physics to Biology. Complexity 12 (4):9-11.
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  32. Peter Aczel, Laura Crosilla, Hajime Ishihara, Erik Palmgren & Peter Schuster (2006). Binary Refinement Implies Discrete Exponentiation. Studia Logica 84 (3):361 - 368.
    Working in the weakening of constructive Zermelo-Fraenkel set theory in which the subset collection scheme is omitted, we show that the binary re.nement principle implies all the instances of the exponentiation axiom in which the basis is a discrete set. In particular binary re.nement implies that the class of detachable subsets of a set form a set. Binary re.nement was originally extracted from the fullness axiom, an equivalent of subset collection, as a principle that was su.cient to prove that the (...)
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  33. Josef Berger, Douglas Bridges & Peter Schuster (2006). The Fan Theorem and Unique Existence of Maxima. Journal of Symbolic Logic 71 (2):713 - 720.
    The existence and uniqueness of a maximum point for a continuous real—valued function on a metric space are investigated constructively. In particular, it is shown, in the spirit of reverse mathematics, that a natural unique existence theorem is equivalent to the fan theorem.
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  34. Josef Berger & Peter Schuster (2006). Classifying Dini's Theorem. Notre Dame Journal of Formal Logic 47 (2):253-262.
    Dini's theorem says that compactness of the domain, a metric space, ensures the uniform convergence of every simply convergent monotone sequence of real-valued continuous functions whose limit is continuous. By showing that Dini's theorem is equivalent to Brouwer's fan theorem for detachable bars, we provide Dini's theorem with a classification in the recently established constructive reverse mathematics propagated by Ishihara. As a complement, Dini's theorem is proved to be equivalent to the analogue of the fan theorem, weak König's lemma, in (...)
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  35. Hajime Ishihara, Ray Mines, Peter Schuster & Luminiţa Vîţă (2006). Quasi-Apartness and Neighbourhood Spaces. Annals of Pure and Applied Logic 141 (1):296-306.
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  36. Peter Schuster (2006). Boltzmann, Atomism, Evolution, and Statistics: Continuity Versus Discreteness in Biology. Complexity 11 (6):9-11.
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  37. Peter Schuster (2006). Formal Zariski Topology: Positivity and Points. Annals of Pure and Applied Logic 137 (1):317-359.
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  38. Peter Schuster (2006). Untamable Curiosity, Innovation, Discovery, and Bricolage: Are We Doomed to Progress to Ever Increasing Complexity? Complexity 11 (5):9-11.
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  39. Peter Schuster (2006). Unique Solutions. Mathematical Logic Quarterly 52 (6):534-539.
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  40. Douglas Bridges, Hajime Ishihara, Peter Schuster & Luminiţa Vîţa (2005). Strong Continuity Implies Uniform Sequential Continuity. Archive for Mathematical Logic 44 (7):887-895.
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  41. Laura Crosilla, Hajime Ishihara & Peter Schuster (2005). On Constructing Completions. Journal of Symbolic Logic 70 (3):969-978.
    The Dedekind cuts in an ordered set form a set in the sense of constructive Zermelo—Fraenkel set theory. We deduce this statement from the principle of refinement, which we distill before from the axiom of fullness. Together with exponentiation, refinement is equivalent to fullness. None of the defining properties of an ordering is needed, and only refinement for two—element coverings is used. In particular, the Dedekind reals form a set; whence we have also refined an earlier result by Aczel and (...)
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  42. Laura Crosilla & Peter Schuster (eds.) (2005). From Sets and Types to Topology and Analysis: Towards Practicable Foundations for Constructive Mathematics. Oxford University Press.
    This edited collection bridges the foundations and practice of constructive mathematics and focuses on the contrast between the theoretical developments, which have been most useful for computer science (ie: constructive set and type theories), and more specific efforts on constructive analysis, algebra and topology. Aimed at academic logician, mathematicians, philosophers and computer scientists with contributions from leading researchers, it is up to date, highly topical and broad in scope.
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  43. Peter Schuster (2005). Evolution and Design: The Darwinian View of Evolution is a Scientific Fact and Not an Ideology. Complexity 11 (1):12-15.
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  44. Peter Schuster (2005). Generation of Information and Complexity: Different Forms of Learning and Innovation: A Simple Mechanism of Learning. Complexity 10 (4):12-14.
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  45. Peter Schuster (2005). “Less is More” and the Art of Modeling Complex Phenomena: Simplification May but Need Not Be the Key to Handle Large Networks. Complexity 11 (2):11-13.
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  46. Peter Schuster (2005). The Commons' Tragicomedy: Self‐Governance Doesn't Come Easily. Complexity 10 (6):10-12.
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  47. Hajime Ishihara & Peter Schuster (2004). Compactness Under Constructive Scrutiny. Mathematical Logic Quarterly 50 (6):540-550.
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  48. Peter Schuster (2004). Chemical Reaction Kinetics is Back: Attempts to Deal with Complexity in Biology: Developing a Quantitative Molecular View to Understanding Life. Complexity 10 (1):14-16.
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  49. Peter Schuster (2004). The Disaster of Central Control. Complexity 9 (4):13-14.
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  50. Peter Schuster (2004). Wolfgang P. Müller, Die Abtreibung: Anfänge der Kriminalisierung, 1140–1650. (Forschungen zur kirchlichen Rechtsgeschichte und zum Kirchenrecht, 24.) Cologne, Weimar, and Vienna: Böhlau, 2000. Paper. Pp. viii, 355. €45. [REVIEW] Speculum 79 (2):530-531.
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