Totality in applicative theories

DOI10.1016/0168-0072(94)00037-4zbMath0832.03027OpenAlexW2007299957MaRDI QIDQ1896484

Thomas Strahm, Gerhard Jäger

Publication date: 5 March 1996

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(94)00037-4

zbMATH Keywords

reductionproof-theoretic strengthaxiom of extensionalityterm modelsapplicative theories of operations and numberstotality of term application

Mathematics Subject Classification ID

Proof theory in general (including proof-theoretic semantics) (03F03)

Related Items (11)

Systems of explicit mathematics with non-constructive \(\mu\)-operator. II ⋮ Polymorphic extensions of simple type structures. With an application to a bar recursive minimization ⋮ Some theories with positive induction of ordinal strength φω0 ⋮ Theories with self-application and computational complexity. ⋮ Polynomial time operations in explicit mathematics ⋮ About Truth and Types ⋮ The Operational Perspective: Three Routes ⋮ The non-constructive \(\mu\) operator, fixed point theories with ordinals, and the bar rule ⋮ Systems of explicit mathematics with non-constructive \(\mu\)-operator and join ⋮ Remarks on applicative theories ⋮ Universes over Frege structures

Cites Work

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• Extended bar induction in applicative theories
• Proof-theoretical analysis: Weak systems of functions and classes
• Constructivism in mathematics. An introduction. Volume II
• Fixed points in Peano arithmetic with ordinals
• Systems of explicit mathematics with non-constructive \(\mu\)-operator. I
• Logical frameworks for truth and abstraction. An axiomatic study
• Hilbert's program relativized; Proof-theoretical and foundational reductions
• Partial Applicative Theories and Explicit Substitutions

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