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Extending the system T0 of explicit mathematics: the limit and Mahlo axioms
Annals of Pure and Applied Logic 114 (1-3):79-101 (2002)
Abstract
In this paper we discuss extensions of Feferman's theory T 0 for explicit mathematics by the so-called limit and Mahlo axioms and present a novel approach to constructing natural recursion-theoretic models for systems of explicit mathematics which is based on nonmonotone inductive definitionsMy notes
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Citations of this work
Does reductive proof theory have a viable rationale?Solomon Feferman - 2000 - Erkenntnis 53 (1-2):63-96.
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.
Decidability for some justification logics with negative introspection.Thomas Studer - 2013 - Journal of Symbolic Logic 78 (2):388-402.
Full operational set theory with unbounded existential quantification and power set.Gerhard Jäger - 2009 - Annals of Pure and Applied Logic 160 (1):33-52.
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.
The strength of some Martin-Löf type theories.Edward Griffor & Michael Rathjen - 1994 - Archive for Mathematical Logic 33 (5):347-385.
Proof-theoretic analysis of KPM.Michael Rathjen - 1991 - Archive for Mathematical Logic 30 (5-6):377-403.
A well-ordering proof for Feferman's theoryT 0.Gerhard Jäger - 1983 - Archive for Mathematical Logic 23 (1):65-77.
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.
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