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  1. Relativizing operational set theory.Gerhard Jäger - 2016 - Bulletin of Symbolic Logic 22 (3):332-352.
    We introduce a way of relativizing operational set theory that also takes care of application. After presenting the basic approach and proving some essential properties of this new form of relativization we turn to the notion of relativized regularity and to the system OST that extends OST by a limit axiom claiming that any set is element of a relativized regular set. Finally we show that OST is proof-theoretically equivalent to the well-known theory KPi for a recursively inaccessible universe.
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  • (1 other version)Explicit mathematics and operational set theory: Some ontological comparisons.Gerhard Jäger & Rico Zumbrunnen - 2014 - Bulletin of Symbolic Logic 20 (3):275-292.
    We discuss several ontological properties of explicit mathematics and operational set theory: global choice, decidable classes, totality and extensionality of operations, function spaces, class and set formation via formulas that contain the definedness predicate and applications.
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  • A new model construction by making a detour via intuitionistic theories I: Operational set theory without choice is Π 1 -equivalent to KP.Kentaro Sato & Rico Zumbrunnen - 2015 - Annals of Pure and Applied Logic 166 (2):121-186.
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