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Reflections on reflections in explicit mathematics
Annals of Pure and Applied Logic 136 (1-2):116-133 (2005)
Abstract
We give a broad discussion of reflection principles in explicit mathematics, thereby addressing various kinds of universe existence principles. The proof-theoretic strength of the relevant systems of explicit mathematics is couched in terms of suitable extensions of Kripke–Platek set theoryMy notes
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Citations of this work
On Feferman’s operational set theory OST.Gerhard Jäger - 2007 - Annals of Pure and Applied Logic 150 (1-3):19-39.
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.
Explicit mathematics and operational set theory: Some ontological comparisons.Gerhard Jäger & Rico Zumbrunnen - 2014 - Bulletin of Symbolic Logic 20 (3):275-292.
A flexible type system for the small Veblen ordinal.Florian Ranzi & Thomas Strahm - 2019 - Archive for Mathematical Logic 58 (5-6):711-751.
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.
Theories for admissible sets: a unifying approach to proof theory.Gerhard Jäger - 1986 - Napoli: Bibliopolis.
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