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Universes in explicit mathematics
Annals of Pure and Applied Logic 109 (3):141-162 (2001)
Abstract
This paper deals with universes in explicit mathematics. After introducing some basic definitions, the limit axiom and possible ordering principles for universes are discussed. Later, we turn to least universes, strictness and name induction. Special emphasis is put on theories for explicit mathematics with universes which are proof-theoretically equivalent to Feferman'sAuthor's Profile
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Review of: Jäger, G.; Kahle, R.; Studer, T.: Universes in explicit mathematics. [REVIEW]Ulrich Wilhelm Kohlenbach - 2002 - Annals of Pure and Applied Logic 109 (3):141-162.
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Citations of this work
Upper Bounds for metapredicative mahlo in explicit mathematics and admissible set theory.Gerhard Jager & Thomas Strahm - 2001 - Journal of Symbolic Logic 66 (2):935-958.
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.
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
A Language and Axioms for Explicit Mathematics.Solomon Feferman, J. N. Crossley, Maurice Boffa, Dirk van Dalen & Kenneth Mcaloon - 1984 - Journal of Symbolic Logic 49 (1):308-311.
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.
The proof-theoretic analysis of transfinitely iterated fixed point theories.Gerhard Jager, Reinhard Kahle, Anton Setzer & Thomas Strahm - 1999 - Journal of Symbolic Logic 64 (1):53-67.
Upper Bounds for metapredicative mahlo in explicit mathematics and admissible set theory.Gerhard Jager & Thomas Strahm - 2001 - Journal of Symbolic Logic 66 (2):935-958.
The strength of Martin-Löf type theory with a superuniverse. Part I.Michael Rathjen - 2000 - Archive for Mathematical Logic 39 (1):1-39.
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