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  1. Relational Dual Tableau Decision Procedures and Their Applications to Modal and Intuitionistic Logics.Joanna Golińska-Pilarek, Taneli Huuskonen & Emilio Muñoz-Velasco - 2014 - Annals of Pure and Applied Logic 165 (2):409-427.
    This paper introduces Basic Intuitionistic Set Theory BIST, and investigates it as a first-order set theory extending the internal logic of elementary toposes. Given an elementary topos, together with the extra structure of a directed structural system of inclusions on the topos, a forcing-style interpretation of the language of first-order set theory in the topos is given, which conservatively extends the internal logic of the topos. This forcing interpretation applies to an arbitrary elementary topos, since any such is equivalent to (...)
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