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  1. Constructive Version of Boolean Algebra.F. Ciraulo, M. E. Maietti & P. Toto - 2013 - Logic Journal of the IGPL 21 (1):44-62.
  • 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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  • Compactness in Locales and in Formal Topology.Steven Vickers - 2006 - Annals of Pure and Applied Logic 137 (1):413-438.
    If a locale is presented by a “flat site”, it is shown how its frame can be presented by generators and relations as a dcpo. A necessary and sufficient condition is derived for compactness of the locale . Although its derivation uses impredicative constructions, it is also shown predicatively using the inductive generation of formal topologies. A predicative proof of the binary Tychonoff theorem is given, including a characterization of the finite covers of the product by basic opens. The discussion (...)
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  • Embedding Locales and Formal Topologies Into Positive Topologies.Francesco Ciraulo & Giovanni Sambin - 2018 - Archive for Mathematical Logic 57 (7-8):755-768.
    A positive topology is a set equipped with two particular relations between elements and subsets of that set: a convergent cover relation and a positivity relation. A set equipped with a convergent cover relation is a predicative counterpart of a locale, where the given set plays the role of a set of generators, typically a base, and the cover encodes the relations between generators. A positivity relation enriches the structure of a locale; among other things, it is a tool to (...)
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  • Spatiality and Classical Logic.Milena Stefanova & Silvio Valentini - 2011 - Mathematical Logic Quarterly 57 (4):432-440.
    In this short note we show that any proof of a general spatiality theorem for inductively generated formal topologies requires full classical logic. © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
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  • Cosheaves and Connectedness in Formal Topology.Steven Vickers - 2012 - Annals of Pure and Applied Logic 163 (2):157-174.