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  1. Giovanni Sambin & Silvio Valentini (forthcoming). Topological Characterization of Scott Domains. Archive for Mathematical Logic.
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  2. Silvio Valentini (2013). Cantor Theorem and Friends, in Logical Form. Annals of Pure and Applied Logic 164 (4):502-508.
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  3. Giovanni Boniolo & Silvio Valentini (2012). Objects: A Study in Kantian Formal Epistemology. Notre Dame Journal of Formal Logic 53 (4):457-478.
    We propose a formal representation of objects , those being mathematical or empirical objects. The powerful framework inside which we represent them in a unique and coherent way is grounded, on the formal side, in a logical approach with a direct mathematical semantics in the well-established field of constructive topology, and, on the philosophical side, in a neo-Kantian perspective emphasizing the knowing subject’s role, which is constructive for the mathematical objects and constitutive for the empirical ones.
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  4. Silvio Valentini (2012). Independence Results in Formal Topology. Annals of Pure and Applied Logic 163 (2):151-156.
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  5. Milena Stefanova & Silvio Valentini (2011). Spatiality and Classical Logic. Mathematical Logic Quarterly 57 (4):432-440.
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  6. Giovanni Boniolo & Silvio Valentini (2008). Vagueness, Kant and Topology: A Study of Formal Epistemology. 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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  7. Silvio Valentini (2007). Constructive Characterizations of Bar Subsets. Annals of Pure and Applied Logic 145 (3):368-378.
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  8. Silvio Valentini (2006). Every Countably Presented Formal Topology is Spatial, Classically. Journal of Symbolic Logic 71 (2):491-500.
    By using some classical reasoning we show that any countably presented formal topology, namely, a formal topology with a countable axiom set, is spatial.
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  9. Silvio Valentini (2005). The Problem of the Formalization of Constructive Topology. Archive for Mathematical Logic 44 (1):115-129.
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  10. Stefano Berardi & Silvio Valentini (2004). Krivine's Intuitionistic Proof of Classical Completeness (for Countable Languages). Annals of Pure and Applied Logic 129 (1-3):93-106.
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  11. Maria Emilia Maietti & Silvio Valentini (2004). A Structural Investigation on Formal Topology: Coreflection of Formal Covers and Exponentiability. Journal of Symbolic Logic 69 (4):967-1005.
    We present and study the category of formal topologies and some of its variants. Two main results are proven. The first is that, for any inductively generated formal cover, there exists a formal topology whose cover extends in the minimal way the given one. This result is obtained by enhancing the method for the inductive generation of the cover relation by adding a coinductive generation of the positivity predicate. Categorically, this result can be rephrased by saying that inductively generated formal (...)
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  12. Thierry Coquand, Giovanni Sambin, Jan Smith & Silvio Valentini (2003). Inductively Generated Formal Topologies. Annals of Pure and Applied Logic 124 (1-3):71-106.
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  13. Silvio Valentini (2002). Extensionality Versus Constructivity. Mathematical Logic Quarterly 48 (2):179-187.
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  14. Silvio Valentini (2002). On the Formal Points of the Formal Topology of the Binary Tree. Archive for Mathematical Logic 41 (7):603-618.
    Formal topology is today an established topic in the development of constructive mathematics and constructive proofs for many classical results of general topology have been obtained by using this approach. Here we analyze one of the main concepts in formal topology, namely, the notion of formal point. We will contrast two classically equivalent definitions of formal points and we will see that from a constructive point of view they are completely different. Indeed, according to the first definition the formal points (...)
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  15. Silvio Valentini (2001). An Elementary Proof of Strong Normalization for Intersection Types. Archive for Mathematical Logic 40 (7):475-488.
    We provide a new and elementary proof of strong normalization for the lambda calculus of intersection types. It uses no strong method, like for instance Tait-Girard reducibility predicates, but just simple induction on type complexity and derivation length and thus it is obviously formalizable within first order arithmetic. To obtain this result, we introduce a new system for intersection types whose rules are directly inspired by the reduction relation. Finally, we show that not only the set of strongly normalizing terms (...)
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  16. Maria Emilia Maietti & Silvio Valentini (1999). Can You Add Power‐Sets to Martin‐Lof's Intuitionistic Set Theory? Mathematical Logic Quarterly 45 (4):521-532.
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  17. Sara Negri & Silvio Valentini (1997). Tychonoff's Theorem in the Framework of Formal Topologies. Journal of Symbolic Logic 62 (4):1315-1332.
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  18. Dario Maguolo & Silvio Valentini (1996). An Intuitionistic Version of Cantor's Theorem. Mathematical Logic Quarterly 42 (1):446-448.
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  19. Silvio Valentini (1996). Decidability in Intuitionistic Type Theory is Functionally Decidable. Mathematical Logic Quarterly 42 (1):300-304.
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  20. Silvio Valentini (1994). Representation Theorems for Quantales. Mathematical Logic Quarterly 40 (2):182-190.
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  21. Ugo Solitro & Silvio Valentini (1993). Local Computation in Linear Logic. Mathematical Logic Quarterly 39 (1):201-212.
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  22. Silvio Valentini (1993). A Proof of the Normal Form Theorem for the Closed Terms of Girard's System F by Means of Computability. Mathematical Logic Quarterly 39 (1):539-544.
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  23. Silvio Valentini (1992). The Judgement Calculus for Intuitionistic Linear Logic: Proof Theory and Semantics. Mathematical Logic Quarterly 38 (1):39-58.
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  24. Silvio Valentini (1983). The Modal Logic of Provability: Cut-Elimination. [REVIEW] Journal of Philosophical Logic 12 (4):471 - 476.
  25. Silvio Valentini (1983). The Modal Logic of Consistency Assertions of Peano Arithmetic. Mathematical Logic Quarterly 29 (1):25-32.
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  26. Giovanni Sambin & Silvio Valentini (1982). The Modal Logic of Provability. The Sequential Approach. Journal of Philosophical Logic 11 (3):311 - 342.