41 found
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  1.  23
    Leo Esakia & Benedikt Löwe (2012). Fatal Heyting Algebras and Forcing Persistent Sentences. 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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  2. Benedikt Löwe & Thomas Müller (eds.) (2010). Phimsamp: Philosophy of Mathematics: Sociological Aspsects and Mathematical Practice. College Publications.
     
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  3.  31
    Benedikt Löwe & Philip D. Welch (2001). Set-Theoretic Absoluteness and the Revision Theory of Truth. 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.  16
    Luca Incurvati & Benedikt Löwe (forthcoming). Restrictiveness Relative to Notions of Interpretation. Review of Symbolic Logic.
    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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  5.  61
    Bernd Buldt, Benedikt Löwe & Thomas Müller (2008). Towards a New Epistemology of Mathematics. 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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  6.  14
    Benedikt Löwe (2006). Set Theory With and Without Urelements and Categories of Interpretations. 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
    Kai-Uwe Kühnberger, Benedikt Löwe, Michael Möllerfeld & Philip Welch (2005). Comparing Inductive and Circular Definitions: Parameters, Complexity and Games. 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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  8.  1
    Benedikt Löwe & Darko Sarenac (2005). Cardinal Spaces and Topological Representations of Bimodal Logics. 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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  9.  12
    Brendan P. Larvor, Benedikt Löwe & Dirk Schlimm (2015). History and Philosophy of Infinity. Synthese 192 (8):2339-2344.
  10.  9
    S. B. Cooper, Benedikt Löwe & Andrea Sorbi (eds.) (2007). New Computational Paradigms: Changing Conceptions of What is Computable. Springer.
    Logicians and theoretical physicists will also benefit from this book.
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  11. Benedikt Löwe, Boris Piwinger & Thoralf Räsch (eds.) (2006). Foundations of the Formal Sciences Iv. The History of the Concept of the Formal Sciences.
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  12.  35
    Benedikt Löwe (2002). The Formal Sciences: Their Scope, Their Foundations, and Their Unity. Synthese 133 (1-2):5 - 11.
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  13.  5
    Jörg Brendle & Benedikt Löwe (1999). Solovay-Type Characterizations for Forcing-Algebras. 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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  14.  66
    Benedikt Löwe & Thomas Müller (2011). Data and Phenomena in Conceptual Modelling. 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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  15. Benedikt Löwe, Wolfgang Malzkorn & Thoralf Räsch (2003). 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] Monograph Collection (Matt - Pseudo).
     
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  16.  24
    Steve Jackson & Benedikt Löwe (2013). Canonical Measure Assignments. 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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  17.  5
    Benedikt Löwe (1998). Uniform Unfolding and Analytic Measurability. 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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  18.  10
    Daisuke Ikegami, David De Kloet & Benedikt Löwe (2012). The Axiom of Real Blackwell Determinacy. 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.  11
    Arnold Beckmann, Costas Dimitracopoulos & Benedikt Löwe (2010). Computability in Europe 2008. Archive for Mathematical Logic 49 (2):119-121.
  20.  7
    Sam Buss, Benedikt Löwe, Dag Normann & Ivan Soskov (2013). Computability in Europe 2011. Annals of Pure and Applied Logic 164 (5):509-510.
  21.  8
    Benedikt Löwe, Florian Rudolph, Andreas Weiermann & Slow Versus Fast Growing (2002). Foundations of the Formal Sciences I. Synthese 133:463-464.
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  22.  4
    Benedikt Löwe (2001). Turing Cones and Set Theory of the Reals. 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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  23.  5
    S. Cooper, Anuj Dawar, Martin Hyland & Benedikt Löwe (2014). Turing Centenary Conference: How the World Computes. Annals of Pure and Applied Logic 165 (9):1353-1354.
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  24.  4
    Benedikt Löwe & Sourav Tarafder (2015). Generalized Algebra-Valued Models of Set Theory. Review of Symbolic Logic 8 (1):192-205.
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  25.  16
    Bernd Buldt, Benedikt Löwe & Thomas Müller (2008). Preface. Erkenntnis 68 (3):305 - 307.
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  26.  3
    Fernando Ferreira, Martin Hyland, Benedikt Löwe & Elvira Mayordomo (2012). Computability in Europe 2010. Annals of Pure and Applied Logic 163 (6):621-622.
  27.  14
    Benedikt Löwe & Thomas Müller (2008). Mathematical Knowledge is Context Dependent. 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.  2
    Benedikt Löwe & Eric Pacuit (2008). An Abstract Approach to Reasoning About Games with Mistaken and Changing Beliefs. Australasian Journal of Logic 6:162-181.
    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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  29.  2
    Klaus Ambos-Spies, Arnold Beckmann, Samuel R. Buss & Benedikt Löwe (2012). Computability in Europe 2009. Annals of Pure and Applied Logic 163 (5):483-484.
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  30.  3
    Benedikt Löwe (2006). A Parametrised Choice Principle and Martin's Conjecture on Blackwell Determinacy. 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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  31.  2
    Benedikt Löwe (2003). A Second Glance at Non-Restrictiveness. Philosophia Mathematica 11 (3):323-331.
    We give an example of a theory that strongly maximizes over ZFC and discuss possible consequences of this finding.
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  32.  3
    Benedikt Löwe (2001). A First Glance at Non-Restrictivenesst. 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. Samuel R. Buss, S. Barry Cooper, Benedikt Löwe & Andrea Sorbi (2009). Preface. Annals of Pure and Applied Logic 160 (3):229-230.
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  34. Karen François, Benedikt Löwe, Thomas Müller & Bart van Kerkhove (eds.) (forthcoming). Foundations of the Formal Sciences VII, Studies in Logic. College Publications.
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  35. Tanmay Inamdar & Benedikt Löwe (2016). The Modal Logic of Inner Models. Journal of Symbolic Logic 81 (1):225-236.
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  36. Benedikt Löwe, Wolfgang Malzkorn & Thoralf Räsch (2003). Foundations of the Formal Sciences II. Applications of Mathematical Logic in Philosophy and Linguistics. Kluwer.
     
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  37. Benedikt Lowe & Thoralf Rasch Malzkorn (2003). Mathematical Logic and Natural Language: Life at the Border. In Benedikt Löwe, Thoralf Räsch & Wolfgang Malzkorn (eds.), Foundations of the Formal Sciences Ii. Kluwer
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  38. Benedikt Lowe, Jan-Willem Romeijn & Eric Pacuit (eds.) (2008). Proceedings of the Foundations of the Formal Sciences VI: Reasoning About Probabilities and Probabilistic Reasoning. College Publications.
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  39. Benedikt Löwe, Thoralf Räsch & Wolfgang Malzkorn (eds.) (2003). Foundations of the Formal Sciences II. Kluwer.
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  40. Benedikt Löwe, Volker Peckhaus & T. Rasch (eds.) (2006). Foundations of the Formal Sciences IV. College Publications.
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  41. Johan van Benthem, Benedikt Lowe & Dov M. Gabbay (eds.) (2008). Interactive Logic: Selected Papers From the 7th Augustus de Morgan Workshop, London. 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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