42 found
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  1. Phimsamp: Philosophy of Mathematics: Sociological Aspsects and Mathematical Practice.Benedikt Löwe & Thomas Müller (eds.) - 2010 - College Publications.
     
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  2.  23
    Fatal Heyting Algebras and Forcing Persistent Sentences.Leo Esakia & Benedikt Löwe - 2012 - Studia Logica 100 (1-2):163-173.
    Hamkins and Löwe proved that the modal logic of forcing is S4.2 . In this paper, we consider its modal companion, the intermediate logic KC and relate it to the fatal Heyting algebra H ZFC of forcing persistent sentences. This Heyting algebra is equationally generic for the class of fatal Heyting algebras. Motivated by these results, we further analyse the class of fatal Heyting algebras.
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  3.  31
    Set-Theoretic Absoluteness and the Revision Theory of Truth.Benedikt Löwe & Philip D. Welch - 2001 - Studia Logica 68 (1):21-41.
    We describe the solution of the Limit Rule Problem of Revision Theory and discuss the philosophical consequences of the fact that the truth set of Revision Theory is a complete 1/2 set.
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  4.  63
    Towards a New Epistemology of Mathematics.Bernd Buldt, Benedikt Löwe & Thomas Müller - 2008 - Erkenntnis 68 (3):309 - 329.
    In this introduction we discuss the motivation behind the workshop “Towards a New Epistemology of Mathematics” of which this special issue constitutes the proceedings. We elaborate on historical and empirical aspects of the desired new epistemology, connect it to the public image of mathematics, and give a summary and an introduction to the contributions to this issue.
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  5.  67
    Data and Phenomena in Conceptual Modelling.Benedikt Löwe & Thomas Müller - 2011 - Synthese 182 (1):131-148.
    The distinction between data and phenomena introduced by Bogen and Woodward (Philosophical Review 97(3):303–352, 1988) was meant to help accounting for scientific practice, especially in relation with scientific theory testing. Their article and the subsequent discussion is primarily viewed as internal to philosophy of science. We shall argue that the data/phenomena distinction can be used much more broadly in modelling processes in philosophy.
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  6.  14
    Set Theory With and Without Urelements and Categories of Interpretations.Benedikt Löwe - 2006 - Notre Dame Journal of Formal Logic 47 (1):83-91.
    We show that the theories ZF and ZFU are synonymous, answering a question of Visser.
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  7.  18
    Restrictiveness Relative to Notions of Interpretation.Luca Incurvati & Benedikt Löwe - 2016 - Review of Symbolic Logic 9 (2): 238-250.
    Maddy gave a semi-formal account of restrictiveness by defining a formal notion based on a class of interpretations and explaining how to handle false positives and false negatives. Recently, Hamkins pointed out some structural issues with Maddy's definition. We look at Maddy's formal definitions from the point of view of an abstract interpretation relation. We consider various candidates for this interpretation relation, including one that is close to Maddy's original notion, but fixes the issues raised by Hamkins. Our work brings (...)
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  8.  18
    Comparing Inductive and Circular Definitions: Parameters, Complexity and Games.Kai-Uwe Kühnberger, Benedikt Löwe, Michael Möllerfeld & Philip Welch - 2005 - Studia Logica 81 (1):79 - 98.
    Gupta-Belnap-style circular definitions use all real numbers as possible starting points of revision sequences. In that sense they are boldface definitions. We discuss lightface versions of circular definitions and boldface versions of inductive definitions.
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  9.  5
    Solovay-Type Characterizations for Forcing-Algebras.Jörg Brendle & Benedikt Löwe - 1999 - Journal of Symbolic Logic 64 (3):1307-1323.
    We give characterizations for the (in ZFC unprovable) sentences "Every Σ 1 2 -set is measurable" and "Every Δ 1 2 -set is measurable" for various notions of measurability derived from well-known forcing partial orderings.
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  10.  1
    Cardinal Spaces and Topological Representations of Bimodal Logics.Benedikt Löwe & Darko Sarenac - 2005 - Logic Journal of the IGPL 13 (3):301-306.
    We look at bimodal logics interpreted by cartesian products of topological spaces and discuss the validity of certain bimodal formulae in products of so-called cardinal spaces. This solves an open problem of van Benthem et al.
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  11.  10
    New Computational Paradigms: Changing Conceptions of What is Computable.S. B. Cooper, Benedikt Löwe & Andrea Sorbi (eds.) - 2007 - Springer.
    Logicians and theoretical physicists will also benefit from this book.
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  12. Foundations of the Formal Sciences Iv. The History of the Concept of the Formal Sciences.Benedikt Löwe, Boris Piwinger & Thoralf Räsch (eds.) - 2006
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  13.  36
    The Formal Sciences: Their Scope, Their Foundations, and Their Unity.Benedikt Löwe - 2002 - Synthese 133 (1-2):5 - 11.
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  14. Foundations of the Formal Sciences Ii Applications of Mathematical Logic in Philosophy and Linguistics : Papers of a Conference Held in Bonn, November 10-13, 2000. [REVIEW]Benedikt Löwe, Wolfgang Malzkorn & Thoralf Räsch - 2003
     
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  15.  16
    History and Philosophy of Infinity.Brendan P. Larvor, Benedikt Löwe & Dirk Schlimm - 2015 - Synthese 192 (8):2339-2344.
  16.  5
    Uniform Unfolding and Analytic Measurability.Benedikt Löwe - 1998 - Archive for Mathematical Logic 37 (8):505-520.
    We generalize Solovay's unfolding technique for infinite games and use an Unfolding Theorem to give a uniform method to prove that all analytic sets are in the $\sigma$ -algebras of measurability connected with well-known forcing notions.
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  17.  24
    Canonical Measure Assignments.Steve Jackson & Benedikt Löwe - 2013 - Journal of Symbolic Logic 78 (2):403-424.
    We work under the assumption of the Axiom of Determinacy and associate a measure to each cardinal $\kappa < \aleph_{\varepsilon_0}$ in a recursive definition of a canonical measure assignment. We give algorithmic applications of the existence of such a canonical measure assignment (computation of cofinalities, computation of the Kleinberg sequences associated to the normal ultrafilters on all projective ordinals).
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  18.  10
    The Axiom of Real Blackwell Determinacy.Daisuke Ikegami, David De Kloet & Benedikt Löwe - 2012 - Archive for Mathematical Logic 51 (7-8):671-685.
    The theory of infinite games with slightly imperfect information has been developed for games with finitely and countably many moves. In this paper, we shift the discussion to games with uncountably many possible moves, introducing the axiom of real Blackwell determinacy ${\mathsf{Bl-AD}_\mathbb{R}}$ (as an analogue of the axiom of real determinacy ${\mathsf{AD}_\mathbb{R}}$ ). We prove that the consistency strength of ${\mathsf{Bl-AD}_\mathbb{R}}$ is strictly greater than that of AD.
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  19.  12
    Computability in Europe 2008.Arnold Beckmann, Costas Dimitracopoulos & Benedikt Löwe - 2010 - Archive for Mathematical Logic 49 (2):119-121.
  20.  8
    Computability in Europe 2011.Sam Buss, Benedikt Löwe, Dag Normann & Ivan Soskov - 2013 - Annals of Pure and Applied Logic 164 (5):509-510.
  21.  8
    Foundations of the Formal Sciences I.Benedikt Löwe, Florian Rudolph, Andreas Weiermann & Slow Versus Fast Growing - 2002 - Synthese 133:463-464.
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  22.  6
    Turing Centenary Conference: How the World Computes.S. Cooper, Anuj Dawar, Martin Hyland & Benedikt Löwe - 2014 - Annals of Pure and Applied Logic 165 (9):1353-1354.
  23.  4
    Turing Cones and Set Theory of the Reals.Benedikt Löwe - 2001 - Archive for Mathematical Logic 40 (8):651-664.
    We investigate Turing cones as sets of reals, and look at the relationship between Turing cones, measures, Baire category and special sets of reals, using these methods to show that Martin's proof of Turing Determinacy (every determined Turing closed set contains a Turing cone or is disjoint from one) does not work when you replace “determined” with “Blackwell determined”. This answers a question of Tony Martin.
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  24.  16
    Preface.Bernd Buldt, Benedikt Löwe & Thomas Müller - 2008 - Erkenntnis 68 (3):305 - 307.
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  25.  4
    Computability in Europe 2010.Fernando Ferreira, Martin Hyland, Benedikt Löwe & Elvira Mayordomo - 2012 - Annals of Pure and Applied Logic 163 (6):621-622.
  26.  4
    Generalized Algebra-Valued Models of Set Theory.Benedikt Löwe & Sourav Tarafder - 2015 - Review of Symbolic Logic 8 (1):192-205.
  27.  14
    Mathematical Knowledge is Context Dependent.Benedikt Löwe & Thomas Müller - 2008 - Grazer Philosophische Studien 76 (1):91-107.
    We argue that mathematical knowledge is context dependent. Our main argument is that on pain of distorting mathematical practice, one must analyse the notion of having available a proof, which supplies justification in mathematics, in a context dependent way.
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  28.  1
    The Modal Logic of Inner Models.Tanmay Inamdar & Benedikt Löwe - 2016 - Journal of Symbolic Logic 81 (1):225-236.
  29.  3
    Computability in Europe 2009.Klaus Ambos-Spies, Arnold Beckmann, Samuel R. Buss & Benedikt Löwe - 2012 - Annals of Pure and Applied Logic 163 (5):483-484.
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  30.  2
    An Abstract Approach to Reasoning About Games with Mistaken and Changing Beliefs.Benedikt Löwe & Eric Pacuit - 2008 - Australasian Journal of Logic 6 (7):162-181.
    We do not believe that logic is the sole answer to deep and intriguing questions about human behaviour, but we think that it might be a useful tool in simulating and understanding it to a certain degree and in specifically restricted areas of application. We do not aim to resolve the question of what rational behaviour in games with mistaken and changing beliefs is. Rather, we develop a formal and abstract framework that allows us to reason about behaviour in games (...)
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  31.  3
    A Parametrised Choice Principle and Martin's Conjecture on Blackwell Determinacy.Benedikt Löwe - 2006 - Mathematical Logic Quarterly 52 (2):187-189.
    We define a parametrised choice principle PCP which is equivalent to the Axiom of Determinacy. PCP describes the difference between these two axioms and could serve as a means of proving Martin's conjecture on the equivalence of these axioms.
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  32.  3
    A First Glance at Non-Restrictivenesst.Benedikt Löwe - 2001 - Philosophia Mathematica 9 (3):347-354.
    Maddy's notion of restrictiveness has many problematic aspects, one of them being that it is almost impossible to show that a theory is not restrictive. In this note the author addresses a crucial question of Martin Goldstern (Vienna) and points to some directions of future research.
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  33. Solovay-Type Characterizations for Forcing-Algebras.Jorg Brendle & Benedikt Lowe - 1999 - Journal of Symbolic Logic 64 (3):1307-1323.
    We give characterizations for the sentences "Every $\Sigma^1_2$-set is measurable" and "Every $\Delta^1_2$-set is measurable" for various notions of measurability derived from well-known forcing partial orderings.
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  34. Preface.Samuel R. Buss, S. Barry Cooper, Benedikt Löwe & Andrea Sorbi - 2009 - Annals of Pure and Applied Logic 160 (3):229-230.
  35. Foundations of the Formal Sciences VII, Studies in Logic.Karen François, Benedikt Löwe, Thomas Müller & Bart van Kerkhove (eds.) - forthcoming - College Publications.
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  36. Foundations of the Formal Sciences II. Applications of Mathematical Logic in Philosophy and Linguistics.Benedikt Löwe, Wolfgang Malzkorn & Thoralf Räsch - 2003 - Kluwer Academic Publishers.
     
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  37. Questions on Generalised Baire Spaces.Yurii Khomskii, Giorgio Laguzzi, Benedikt Löwe & Ilya Sharankou - 2016 - Mathematical Logic Quarterly 62 (4-5):439-456.
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  38. Mathematical Logic and Natural Language: Life at the Border.Benedikt Lowe & Thoralf Rasch Malzkorn - 2003 - In Benedikt Löwe, Thoralf Räsch & Wolfgang Malzkorn (eds.), Foundations of the Formal Sciences Ii. Kluwer Academic Publishers.
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  39. Proceedings of the Foundations of the Formal Sciences VI: Reasoning About Probabilities and Probabilistic Reasoning.Benedikt Lowe, Jan-Willem Romeijn & Eric Pacuit (eds.) - 2008 - College Publications.
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  40. Foundations of the Formal Sciences II.Benedikt Löwe, Thoralf Räsch & Wolfgang Malzkorn (eds.) - 2003 - Kluwer Academic Publishers.
  41. Foundations of the Formal Sciences IV.Benedikt Löwe, Volker Peckhaus & T. Rasch (eds.) - 2006 - College Publications.
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  42. Interactive Logic: Selected Papers From the 7th Augustus de Morgan Workshop, London.Johan van Benthem, Benedikt Lowe & Dov M. Gabbay (eds.) - 2008 - Amsterdam University Press.
    This collection of papers from the workshop serves as the initial volume in the new series Texts in Logics and Games—touching on research in logic, mathematics, computer science, and game theory. “A wonderful demonstration of ...
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