EXPLICIT MATHEMATICS AND OPERATIONAL SET THEORY: SOME ONTOLOGICAL COMPARISONS

DOI10.1017/BSL.2014.21zbMath1345.03112OpenAlexW2057062089MaRDI QIDQ2795201

Rico Zumbrunnen, Gerhard Jäger

Publication date: 18 March 2016

Published in: The Bulletin of Symbolic Logic (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/bsl.2014.21

zbMATH Keywords

explicit mathematicsoperational set theory

Mathematics Subject Classification ID

Nonclassical and second-order set theories (03E70) Metamathematics of constructive systems (03F50)

Related Items (5)

RELATIVIZING OPERATIONAL SET THEORY ⋮ A new model construction by making a detour via intuitionistic theories. I: Operational set theory without choice is \(\Pi_1\)-equivalent to KP ⋮ Applicable Mathematics in a Minimal Computational Theory of Sets ⋮ The Operational Penumbra: Some Ontological Aspects ⋮ A new model construction by making a detour via intuitionistic theories. II: Interpretability lower bound of Feferman's explicit mathematics \(T_0\)

Cites Work

• Operational closure and stability
• Operational set theory and small large cardinals
• Full operational set theory with unbounded existential quantification and power set
• Towards a computation system based on set theory
• Systems of explicit mathematics with non-constructive \(\mu\)-operator. II
• On Feferman's operational set theory \textsf{OST}
• Reflections on reflections in explicit mathematics
• Upper bounds for metapredicative Mahlo in explicit mathematics and admissible set theory
• Extending constructive operational set theory by impredicative principles
• Power types in explicit mathematics?
• Extending the system T\(_0\) of explicit mathematics: The limit and Mahlo axioms

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