Some theories with positive induction of ordinal strength φω0

DOI10.2307/2275787zbMath0862.03031OpenAlexW1519442806MaRDI QIDQ5687318

Thomas Strahm, Gerhard Jäger

Publication date: 12 December 1996

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

Full work available at URL: https://doi.org/10.2307/2275787

zbMATH Keywords

proof-theoretic strengthapplicative theoriesrestricted inductionfixed point theories with ordinalsnonconstructive \(\mu\) operatorsubtheory of Peano arithmetic

Mathematics Subject Classification ID

First-order arithmetic and fragments (03F30) Recursive ordinals and ordinal notations (03F15)

Related Items (8)

Theories with self-application and computational complexity. ⋮ A new model construction by making a detour via intuitionistic theories. I: Operational set theory without choice is \(\Pi_1\)-equivalent to KP ⋮ A note on the theory of positive induction, \({{\text{ID}}^*_1}\) ⋮ An ordinal analysis for theories of self-referential truth ⋮ PROOF-THEORETIC STRENGTHS OF WEAK THEORIES FOR POSITIVE INDUCTIVE DEFINITIONS ⋮ 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 ⋮ Universes over Frege structures

Cites Work

• Fragments of arithmetic
• Constructivism in mathematics. An introduction. Volume I
• Fixed points in Peano arithmetic with ordinals
• Systems of explicit mathematics with non-constructive \(\mu\)-operator. I
• Totality in applicative theories
• Second order theories with ordinals and elementary comprehension
• Notes on Formal Theories of Truth
• Beweistheorie vonKPN

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