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Explicit mathematics and operational set theory: Some ontological comparisons
Bulletin of Symbolic Logic 20 (3):275-292 (2014)
Abstract
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.Links
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Citations of this work
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.
A new model construction by making a detour via intuitionistic theories II: Interpretability lower bound of Feferman's explicit mathematics T 0.Kentaro Sato - 2015 - Annals of Pure and Applied Logic 166 (7-8):800-835.
References found in this work
Systems of explicit mathematics with non-constructive μ-operator. Part II.Solomon Feferman & Gerhard Jäger - 1996 - Annals of Pure and Applied Logic 79 (1):37-52.
Upper Bounds for metapredicative mahlo in explicit mathematics and admissible set theory.Gerhard Jäger & Thomas Strahm - 2001 - Journal of Symbolic Logic 66 (2):935-958.
On Feferman’s operational set theory OST.Gerhard Jäger - 2007 - Annals of Pure and Applied Logic 150 (1-3):19-39.
Extending the system T0 of explicit mathematics: the limit and Mahlo axioms.Gerhard Jäger & Thomas Studer - 2002 - Annals of Pure and Applied Logic 114 (1-3):79-101.
Full operational set theory with unbounded existential quantification and power set.Gerhard Jäger - 2009 - Annals of Pure and Applied Logic 160 (1):33-52.
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