Results for 'Topology'

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  1. The Topology of Communities of Trust.Mark Alfano - 2016 - Russian Sociological Review 15 (4):30-56.
    Hobbes emphasized that the state of nature is a state of war because it is characterized by fundamental and generalized distrust. Exiting the state of nature and the conflicts it inevitably fosters is therefore a matter of establishing trust. Extant discussions of trust in the philosophical literature, however, focus either on isolated dyads of trusting individuals or trust in large, faceless institutions. In this paper, I begin to fill the gap between these extremes by analyzing what I call the (...) of communities of trust. Such communities are best understood in terms of interlocking dyadic relationships that approximate the ideal of being symmetric, Euclidean, reflexive, and transitive. Few communities of trust live up to this demanding ideal, and those that do tend to be small (between three and fifteen individuals). Nevertheless, such communities of trust serve as the conditions for the possibility of various important prudential epistemic, cultural, and mental health goods. However, communities of trust also make possible various problematic phenomena. They can become insular and walled-off from the surrounding community, leading to distrust of out-groups. And they can lead their members to abandon public goods for tribal or parochial goods. These drawbacks of communities of trust arise from some of the same mecha-nisms that give them positive prudential, epistemic, cultural, and mental health value – and so can at most be mitigated, not eliminated. (shrink)
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  2.  90
    Similarity, Topology, and Physical Significance in Relativity Theory.Samuel C. Fletcher - 2016 - British Journal for the Philosophy of Science 67 (2):365-389.
    Stephen Hawking, among others, has proposed that the topological stability of a property of space-time is a necessary condition for it to be physically significant. What counts as stable, however, depends crucially on the choice of topology. Some physicists have thus suggested that one should find a canonical topology, a single ‘right’ topology for every inquiry. While certain such choices might be initially motivated, some little-discussed examples of Robert Geroch and some propositions of my own show that (...)
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  3.  8
    Tame Topology Over Dp-Minimal Structures.Pierre Simon & Erik Walsberg - 2019 - Notre Dame Journal of Formal Logic 60 (1):61-76.
    In this article, we develop tame topology over dp-minimal structures equipped with definable uniformities satisfying certain assumptions. Our assumptions are enough to ensure that definable sets are tame: there is a good notion of dimension on definable sets, definable functions are almost everywhere continuous, and definable sets are finite unions of graphs of definable continuous “multivalued functions.” This generalizes known statements about weakly o-minimal, C-minimal, and P-minimal theories.
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  4. Time, Topology and Physical Geometry.Tim Maudlin - 2010 - Aristotelian Society Supplementary Volume 84 (1):63-78.
    The standard mathematical account of the sub-metrical geometry of a space employs topology, whose foundational concept is the open set. This proves to be an unhappy choice for discrete spaces, and offers no insight into the physical origin of geometrical structure. I outline an alternative, the Theory of Linear Structures, whose foundational concept is the line. Application to Relativistic space-time reveals that the whole geometry of space-time derives from temporal structure. In this sense, instead of spatializing time, Relativity temporalizes (...)
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  5. Topology as an Issue for History of Philosophy of Science.Thomas Mormann - 2013 - In Hanne Andersen, Dennis Dieks, Wenceslao J. Gonzalez, Thomas Uebel & Gregory Wheeler (eds.), New Challenges to Philosophy of Science. Springer. pp. 423--434.
    Since antiquity well into the beginnings of the 20th century geometry was a central topic for philosophy. Since then, however, most philosophers of science, if they took notice of topology at all, considered it as an abstruse subdiscipline of mathematics lacking philosophical interest. Here it is argued that this neglect of topology by philosophy may be conceived of as the sign of a conceptual sea-change in philosophy of science that expelled geometry, and, more generally, mathematics, from the central (...)
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  6. Gunk, Topology and Measure.Frank Arntzenius - 2004 - In Dean Zimmerman (ed.), Oxford Studies in Metaphysics: Volume 4. Oxford University Press.
    I argue that it may well be the case that space and time do not consist of points, indeed that they have no smallest parts. I examine two different approaches to such pointless spaces : a topological approach and a measure theoretic approach. I argue in favor of the measure theoretic approach.
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  7.  39
    Measure, Topology and Probabilistic Reasoning in Cosmology.Erik Curiel - unknown
    I explain the difficulty of making various concepts of and relating to probability precise, rigorous and physically significant when attempting to apply them in reasoning about objects living in infinite-dimensional spaces, working through many examples from cosmology. I focus on the relation of topological to measure-theoretic notions of and relating to probability, how they diverge in unpleasant ways in the infinite-dimensional case, and are even difficult to work with on their own. Even in cases where an appropriate family of spacetimes (...)
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  8.  24
    Heidegger's Topology: Being, Place, World.Jeff Malpas - 2006 - Bradford.
    This groundbreaking inquiry into the centrality of place in Martin Heidegger's thinking offers not only an illuminating reading of Heidegger's thought but a detailed investigation into the way in which the concept of place relates to core philosophical issues. In Heidegger's Topology, Jeff Malpas argues that an engagement with place, explicit in Heidegger's later work, informs Heidegger's thought as a whole. What guides Heidegger's thinking, Malpas writes, is a conception of philosophy's starting point: our finding ourselves already "there," situated (...)
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  9.  35
    Apartness, Topology, and Uniformity: A Constructive View.Douglas Bridges, Peter Schuster & Luminiţa Vîţă - 2002 - Mathematical Logic Quarterly 48 (4):16-28.
    The theory of apartness spaces, and their relation to topological spaces (in the point–set case) and uniform spaces (in the set–set case), is sketched. New notions of local decomposability and regularity are investigated, and the latter is used to produce an example of a classically metrisable apartness on R that cannot be induced constructively by a uniform structure.
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  10.  23
    Cultural Topology: The Seven Bridges of Königsburg, 1736.Rob Shields - 2012 - Theory, Culture and Society 29 (4-5):43-57.
    In an example of Enlightenment ‘engaged research' and public intellectual practice, Euler established the basis of topology and graph theory through his solution to the puzzle of whether a stroll around the seven bridges of 18th-century Königsberg was possible without having to cross any given bridge twice. This ‘Manifesto' argues that, born in a form of cultural studies, topology offers 21st-century researchers a model for mapping the dynamics of time as well as space, allowing the rigorous description of (...)
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  11.  23
    Topology and Duality in Modal Logic.Giovanni Sambin & Virginia Vaccaro - 1988 - Annals of Pure and Applied Logic 37 (3):249-296.
  12.  8
    Topology Via Logic.P. T. Johnstone & Steven Vickers - 1991 - Journal of Symbolic Logic 56 (3):1101.
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  13. Events, Topology and Temporal Relations.Fabio Pianesi & Achille C. Varzi - 1996 - The Monist 79 (1):89--116.
    We are used to regarding actions and other events, such as Brutus’ stabbing of Caesar or the sinking of the Titanic, as occupying intervals of some underlying linearly ordered temporal dimension. This attitude is so natural and compelling that one is tempted to disregard the obvious difference between time periods and actual happenings in favor of the former: events become mere “intervals cum description”.1 On the other hand, in ordinary circumstances the point of talking about time is to talk about (...)
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  14. Topology Change and the Unity of Space.Craig Callender & Robert Weingard - 2000 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 31 (2):227-246.
    Must space be a unity? This question, which exercised Aristotle, Descartes and Kant, is a specific instance of a more general one; namely, can the topology of physical space change with time? In this paper we show how the discussion of the unity of space has been altered but survives in contemporary research in theoretical physics. With a pedagogical review of the role played by the Euler characteristic in the mathematics of relativistic spacetimes, we explain how classical general relativity (...)
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  15.  51
    Topology as Epistemology.Cory Juhl - 1996 - The Monist 79 (1):141-147.
    From one perspective, the fundamental notions of point-set topology have to do with sequences and their limits. A broad class of epistemological questions also appear to be concerned with sequences and their limits. For example, problems of empirical underdetermination—which of a collection of alternative theories is true—have to do with logical properties of sequences of evidence. Underdetermination by evidence is the central problem of Plato’s Meno, of one of Sextus Empiricus’ many skeptical doubts, and arguably it is the idea (...)
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  16.  16
    Modern Topology and Peirce's Theory of the Continuum.Arnold Johanson - 2001 - Transactions of the Charles S. Peirce Society 37 (1):1 - 12.
  17.  79
    Topology, Empiricism, and Operationalism.Ernest W. Adams - 1996 - The Monist 79 (1):1--20.
    How do concepts of topology such as that of a boundary apply to the empirical world? Take the example of a chess board, represented here with black squares in black and red squares in white. We see by looking at the board that the squares of any one color have common boundaries only with squares of the opposite color, but each square has corners in common with other squares of the same color, which are points at which their common (...)
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  18. Topology and Life Redux: Robert Rosen’s Relational Diagrams of Living Systems. [REVIEW]A. H. Louie & Stephen W. Kercel - 2007 - Axiomathes 17 (2):109-136.
    Algebraic/topological descriptions of living processes are indispensable to the understanding of both biological and cognitive functions. This paper presents a fundamental algebraic description of living/cognitive processes and exposes its inherent ambiguity. Since ambiguity is forbidden to computation, no computational description can lend insight to inherently ambiguous processes. The impredicativity of these models is not a flaw, but is, rather, their strength. It enables us to reason with ambiguous mathematical representations of ambiguous natural processes. The noncomputability of these structures means computerized (...)
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  19. A Topology of the Teaching Concept.Thomas F. Green - 1964 - Studies in Philosophy and Education 3 (4):284-319.
  20. Topology and Modality: The Topological Interpretation of First-Order Modal Logic: Topology and Modality.Steve Awodey - 2008 - Review of Symbolic Logic 1 (2):146-166.
    As McKinsey and Tarski showed, the Stone representation theorem for Boolean algebras extends to algebras with operators to give topological semantics for propositional modal logic, in which the “necessity” operation is modeled by taking the interior of an arbitrary subset of a topological space. In this article, the topological interpretation is extended in a natural way to arbitrary theories of full first-order logic. The resulting system of S4 first-order modal logic is complete with respect to such topological semantics.
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  21.  73
    Topology, Cosmology and Convention.Clark Glymour - 1972 - Synthese 24 (1-2):195 - 218.
  22.  91
    Region-Based Topology.Peter Roeper - 1997 - Journal of Philosophical Logic 26 (3):251-309.
    A topological description of space is given, based on the relation of connection among regions and the property of being limited. A minimal set of 10 constraints is shown to permit definitions of points and of open and closed sets of points and to be characteristic of locally compact T2 spaces. The effect of adding further constraints is investigated, especially those that characterise continua. Finally, the properties of mappings in region-based topology are studied. Not all such mappings correspond to (...)
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  23. On Continuity: Aristotle Versus Topology?Michael J. White - 1988 - History and Philosophy of Logic 9 (1):1-12.
    This paper begins by pointing out that the Aristotelian conception of continuity (synecheia) and the contemporary topological account share the same intuitive, proto-topological basis: the conception of a ?natural whole? or unity without joints or seams. An argument of Aristotle to the effect that what is continuous cannot be constituted of ?indivisibles? (e.g., points) is examined from a topological perspective. From that perspective, the argument fails because Aristotle does not recognize a collective as well as a distributive concept of a (...)
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  24.  8
    Topology and Morphogenesis.X. W. Sha - 2012 - Theory, Culture and Society 29 (4-5):220-246.
    One can use mathematics not as an instrument or measure, or a replacement for God, but as a poetic articulation, or perhaps as a stammered experimental approach to cultural dynamics. I choose to start with the simplest symbolic substances that respect the lifeworld’s continuous dynamism, temporality, boundless morphogenesis, superposability, continuity, density and value, and yet are independent of measure, metric, counting, finitude, formal logic, syntax, grammar, digitality and computability – in short, free of the formal structures that would put a (...)
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  25.  20
    A Topology for Galois Types in Abstract Elementary Classes.Michael Lieberman - 2011 - Mathematical Logic Quarterly 57 (2):204-216.
    We present a way of topologizing sets of Galois types over structures in abstract elementary classes with amalgamation. In the elementary case, the topologies thus produced refine the syntactic topologies familiar from first order logic. We exhibit a number of natural correspondences between the model-theoretic properties of classes and their constituent models and the topological properties of the associated spaces. Tameness of Galois types, in particular, emerges as a topological separation principle. © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
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  26.  45
    Aspects of General Topology in Constructive Set Theory.Peter Aczel - 2006 - Annals of Pure and Applied Logic 137 (1-3):3-29.
    Working in constructive set theory we formulate notions of constructive topological space and set-generated locale so as to get a good constructive general version of the classical Galois adjunction between topological spaces and locales. Our notion of constructive topological space allows for the space to have a class of points that need not be a set. Also our notion of locale allows the locale to have a class of elements that need not be a set. Class sized mathematical structures need (...)
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  27.  48
    Physical Topology.Chris Mortensen & Graham Nerlich - 1978 - Journal of Philosophical Logic 7 (1):209 - 223.
  28.  99
    Vagueness, Kant and Topology: A Study of Formal Epistemology.Giovanni Boniolo & Silvio Valentini - 2008 - Journal of Philosophical Logic 37 (2):141-168.
    In this paper we propose an approach to vagueness characterised by two features. The first one is philosophical: we move along a Kantian path emphasizing the knowing subject’s conceptual apparatus. The second one is formal: to face vagueness, and our philosophical view on it, we propose to use topology and formal topology. We show that the Kantian and the topological features joined together allow us an atypical, but promising, way of considering vagueness.
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  29. Hyperstructures, Topology and Datasets.Nils A. Baas - 2009 - Axiomathes 19 (3):281-295.
    In the natural sciences higher order structures often occur. There seems to be a need for good methods of describing what we mean by higher order structures in various contexts. This is what hyperstructures are intended to do. We motivate and introduce this new concept. Next we illustrate how it can be applied in various types of genomic analysis—particular the correlations between single nucleotide polymorphisms and diseases. The suggested structure is quite general and may be applied to a variety of (...)
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  30.  36
    The Algebra of Topology.J. C. C. Mckinsey & Alfred Tarski - 1944 - Annals of Mathematics, Second Series 45:141-191.
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  31.  12
    The Canonical Topology on Dp-Minimal Fields.Will Johnson - 2018 - Journal of Mathematical Logic 18 (2):1850007.
    We construct a nontrivial definable type V field topology on any dp-minimal field K that is not strongly minimal, and prove that definable subsets of Kn have small boundary. Using this topology and...
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  32.  18
    Grothendieck Topology as Geometric Modality.Robert I. Goldblatt - 1981 - Mathematical Logic Quarterly 27 (31‐35):495-529.
  33.  25
    Grothendieck Topology as Geometric Modality.Robert I. Goldblatt - 1981 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 27 (31-35):495-529.
  34.  21
    Nonstandard Topology and Extensions of Monad Systems to Infinite Points.Frank Wattenberg - 1971 - Journal of Symbolic Logic 36 (3):463-476.
  35. Indivisible Parts and Extended Objects: Some Philosophical Episodes From Topology’s Prehistory.Dean W. Zimmerman - 1996 - The Monist 79 (1):148--80.
    Physical boundaries and the earliest topologists. Topology has a relatively short history; but its 19th century roots are embedded in philosophical problems about the nature of extended substances and their boundaries which go back to Zeno and Aristotle. Although it seems that there have always been philosophers interested in these matters, questions about the boundaries of three-dimensional objects were closest to center stage during the later medieval and modern periods. Are the boundaries of an object actually existing, less-than-three-dimensional parts (...)
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  36.  9
    Modal Languages for Topology: Expressivity and Definability.Balder ten Cate, David Gabelaia & Dmitry Sustretov - 2009 - Annals of Pure and Applied Logic 159 (1-2):146-170.
    In this paper we study the expressive power and definability for modal languages interpreted on topological spaces. We provide topological analogues of the van Benthem characterization theorem and the Goldblatt–Thomason definability theorem in terms of the well-established first-order topological language.
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  37.  43
    The Topology of Time: An Analysis of Medieval Islamic Accounts of Discrete and Continuous Time.Jon McGinnis - 2003 - Modern Schoolman 81 (1):5-25.
  38.  11
    Fuzzy Topology Representation for MV‐Algebras.Jialu Zhang & Quanfa Chen - 2009 - Mathematical Logic Quarterly 55 (3):259-270.
    Let M be an MV-algebra and ΩM be the set of all σ -valuations from M into the MV-unit interval. This paper focuses on the characterization of MV-algebras using σ -valuations of MV-algebras and proves that a σ -complete MV-algebra is σ -regular, which means that a ≤ b if and only if v ≤ v for any v ∈ ΩM. Then one can introduce in a natural way a fuzzy topology δ on ΩM. The representation theorem forMV-algebras is (...)
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  39. Set Theory, Topology, and the Possibility of Junky Worlds.Thomas Mormann - 2014 - Notre Dame Journal of Formal Logic 55 (1): 79 - 90.
    A possible world is a junky world if and only if each thing in it is a proper part. The possibility of junky worlds contradicts the principle of general fusion. Bohn (2009) argues for the possibility of junky worlds, Watson (2010) suggests that Bohn‘s arguments are flawed. This paper shows that the arguments of both authors leave much to be desired. First, relying on the classical results of Cantor, Zermelo, Fraenkel, and von Neumann, this paper proves the possibility of junky (...)
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  40.  87
    Genidentity and Topology of Time: Kurt Lewin and Hans Reichenbach.Flavia Padovani - unknown
    In the early 1920s, Hans Reichenbach and Kurt Lewin presented two topological accounts of time that appear to be interrelated in more than one respect. Despite their different approaches, their underlying idea is that time order is derived from specific structural properties of the world. In both works, moreover, the notion of genidentity--i.e., identity through or over time--plays a crucial role. Although it is well known that Reichenbach borrowed this notion from Kurt Lewin, not much has been written about their (...)
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  41. The Naive Topology of the Conscious Subject.Rory Madden - 2015 - Noûs 49 (1):55-70.
    What does our naïve conception of a conscious subject demand of the nature of conscious beings? In a series of recent papers David Barnett has argued that a range of powerful intuitions in the philosophy of mind are best explained by the hypothesis that our naïve conception imposes a requirement of mereological simplicity on the nature of conscious beings. It is argued here that there is a much more plausible explanation of the intuitions in question. Our naïve conception of a (...)
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  42.  7
    Deforming the Figure: Topology and the Social Imaginary.Scott Lash - 2012 - Theory, Culture and Society 29 (4-5):261-287.
    Topology is integral to a shift in socio-cultural theory from a linguistic to a mathematical paradigm. This has enabled in Badiou and Žižek a critique of the symbolic register, understood in terms of pure conceptual abstraction. Drawing on topology, this article understands it instead in terms of the figure. The break with the symbolic and language necessitates a break with form, but topologically still preserves a logic of the figure. This becomes a process of figuration, indeed a process (...)
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  43. Time, Topology, and the Twin Paradox.Jean-Pierre Luminet - 2011 - In Craig Callender (ed.), The Oxford Handbook of Philosophy of Time. Oxford University Press.
  44.  50
    Regular Opens in Constructive Topology and a Representation Theorem for Overlap Algebras.Francesco Ciraulo - 2013 - Annals of Pure and Applied Logic 164 (4):421-436.
    Giovanni Sambin has recently introduced the notion of an overlap algebra in order to give a constructive counterpart to a complete Boolean algebra. We propose a new notion of regular open subset within the framework of intuitionistic, predicative topology and we use it to give a representation theorem for overlap algebras. In particular we show that there exists a duality between the category of set-based overlap algebras and a particular category of topologies in which all open subsets are regular.
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  45.  25
    The Topology of Des Hegemonies Brisées.Reginald Lilly - 1998 - Research in Phenomenology 28 (1):226-242.
  46.  14
    Logic and Topology for Knowledge, Knowability, and Belief.Adam Bjorndahl & Aybüke Özgün - 2020 - Review of Symbolic Logic 13 (4):748-775.
    In recent work, Stalnaker proposes a logical framework in which belief is realized as a weakened form of knowledge 35. Building on Stalnaker’s core insights, and using frameworks developed in 11 and 3, we employ topological tools to refine and, we argue, improve on this analysis. The structure of topological subset spaces allows for a natural distinction between what is known and what is knowable; we argue that the foundational axioms of Stalnaker’s system rely intuitively on both of these notions. (...)
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  47.  51
    Simplicity in Effective Topology.Iraj Kalantari & Anne Leggett - 1982 - Journal of Symbolic Logic 47 (1):169-183.
    The recursion-theoretic study of mathematical structures other thanωis now a field of much activity. Analysis and algebra are two such structures which have been studied for their effective contents. Studies in analysis began with the work of Specker on nonconstructive proofs in analysis [16] and in Lacombe's inspiring notes on relevant notions of recursive analysis [8]. Studies in algebra originated in the work of Frolich and Shepherdson on effective extensions of explicit fields [1] and in Rabin's study of computable fields (...)
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  48.  14
    Sublocales in Formal Topology.Steven Vickers - 2007 - Journal of Symbolic Logic 72 (2):463 - 482.
    The paper studies how the localic notion of sublocale transfers to formal topology. For any formal topology (not necessarily with positivity predicate) we define a sublocale to be a cover relation that includes that of the formal topology. The family of sublocales has set-indexed joins. For each set of base elements there are corresponding open and closed sublocales, boolean complements of each other. They generate a boolean algebra amongst the sublocales. In the case of an inductively generated (...)
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  49.  33
    A Generalized Manifold Topology for Branching Space-Times.Thomas Müller - 2013 - Philosophy of Science 80 (5):1089-1100.
    The logical theory of branching space-times, which provides a relativistic framework for studying objective indeterminism, remains mostly disconnected from discussions of space-time theories in philosophy of physics. Earman has criticized the branching approach and suggested “pruning some branches from branching space-time.” This article identifies the different—order-theoretic versus topological—perspective of both discussions as a reason for certain misunderstandings and tries to remove them. Most important, we give a novel, topological criterion of modal consistency that usefully generalizes an earlier criterion, and we (...)
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  50.  4
    On the Forking Topology of a Reduct of a Simple Theory.Ziv Shami - 2020 - Archive for Mathematical Logic 59 (3-4):313-324.
    Let T be a simple L-theory and let \ be a reduct of T to a sublanguage \ of L. For variables x, we call an \-invariant set \\) in \ a universal transducer if for every formula \\in L^-\) and every a, $$\begin{aligned} \phi ^-\ L^-\text{-forks } \text{ over }\ \emptyset \ \text{ iff } \Gamma \wedge \phi ^-\ L\text{-forks } \text{ over }\ \emptyset. \end{aligned}$$We show that there is a greatest universal transducer \ and it is type-definable. In (...)
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