Explicit mathematics with the monotone fixed point principle

DOI10.2307/2586846zbMath0912.03028OpenAlexW2002495770MaRDI QIDQ4212918

Michael Rathjen

Publication date: 16 May 1999

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

Full work available at URL: https://doi.org/10.2307/2586846

zbMATH Keywords

explicit mathematicsmonotone fixed point principleproof-theoretic reducibility

Mathematics Subject Classification ID

Second- and higher-order arithmetic and fragments (03F35) Metamathematics of constructive systems (03F50)

Related Items (5)

ABOUT SOME FIXED POINT AXIOMS AND RELATED PRINCIPLES IN KRIPKE–PLATEK ENVIRONMENTS ⋮ The Operational Penumbra: Some Ontological Aspects ⋮ Proof Theory of Constructive Systems: Inductive Types and Univalence ⋮ On the Strength of the Uniform Fixed Point Principle in Intuitionistic Explicit Mathematics ⋮ A new model construction by making a detour via intuitionistic theories. II: Interpretability lower bound of Feferman's explicit mathematics \(T_0\)

Cites Work

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• Monotone inductive definitions in a constructive theory of functions and classes
• On the proof-theoretic strength of monotone induction in explicit mathematics
• The syntax and semantics of infinitary languages
• The Shoenfield absoluteness lemma
• Recursion in Kolmogorov's R-operator and the ordinal σ₃

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