Monotone inductive definitions in a constructive theory of functions and classes

DOI10.1016/0168-0072(89)90019-5zbMath0665.03037OpenAlexW2035074687WikidataQ127207371 ScholiaQ127207371MaRDI QIDQ1115865

Shuzo Takahashi

Publication date: 1989

Published in: Annals of Pure and Applied Logic (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0168-0072(89)90019-5

zbMATH Keywords

proof-theoretic strengthcombinatorsconstructive theory of functions and classesleast fixed point principlemonotone inductive definitions

Mathematics Subject Classification ID

Other constructive mathematics (03F65) Inductive definability (03D70) Abstract and axiomatic computability and recursion theory (03D75)

Related Items (11)

Understanding uniformity in Feferman's explicit mathematics ⋮ On the proof-theoretic strength of monotone induction in explicit mathematics ⋮ On the intuitionistic strength of monotone inductive definitions ⋮ On power set in explicit mathematics ⋮ The Operational Perspective: Three Routes ⋮ The Operational Penumbra: Some Ontological Aspects ⋮ Proof Theory of Constructive Systems: Inductive Types and Univalence ⋮ Systems of explicit mathematics with non-constructive \(\mu\)-operator and join ⋮ Explicit mathematics with the monotone fixed point principle ⋮ 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

• Iterated inductive definitions and subsystems of analysis: recent proof-theoretical studies
• Effective operations on partial recursive functions
• Abstract First Order Computability. I
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