Fragments of arithmetic

DOI10.1016/0168-0072(85)90030-2zbMath0558.03029OpenAlexW2038447110MaRDI QIDQ762484

Wilfried Sieg

Publication date: 1985

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(85)90030-2

zbMATH Keywords

fragments of arithmeticfinitary proofsoperator theoriessubsystems of analysis

Mathematics Subject Classification ID

First-order arithmetic and fragments (03F30) Second- and higher-order arithmetic and fragments (03F35) Relative consistency and interpretations (03F25)

Related Items (35)

Separation and Weak König's Lemma ⋮ Predicative foundations of arithmetic ⋮ Majorizing provably recursive functions in fragments of PA ⋮ European Summer Meeting of the Association for Symbolic Logic ⋮ Iterated local reflection versus iterated consistency ⋮ Herbrand analyses ⋮ Induction rules, reflection principles, and provably recursive functions ⋮ Hilbert's program and the omega-rule ⋮ Finite left-distributive algebras and embedding algebras ⋮ Fluctuations, effective learnability and metastability in analysis ⋮ Effective bounds from ineffective proofs in analysis: An application of functional interpretation and majorization ⋮ Left-distributive embedding algebras ⋮ Baire categoricity and \(\Sigma_1^0\)-induction ⋮ How to characterize provably total functions by local predicativity ⋮ Bimodal logics for extensions of arithmetical theories ⋮ Some theories with positive induction of ordinal strength φω0 ⋮ Theories with self-application and computational complexity. ⋮ Things that can and things that cannot be done in PRA ⋮ Hilbert versus Hindman ⋮ Ordinal numbers and the Hilbert basis theorem ⋮ Harrington's conservation theorem redone ⋮ On mathematical instrumentalism ⋮ A simple proof of Parsons' theorem ⋮ On uniform weak König's lemma ⋮ UNFOLDING FINITIST ARITHMETIC ⋮ Extensions of the Finitist Point of View ⋮ The logic of \(\Pi_ 1\)-conservativity ⋮ Remarks on Herbrand normal forms and Herbrand realizations ⋮ Which set existence axioms are needed to prove the separable Hahn-Banach theorem? ⋮ European Summer Meeting of the Association for Symbolic Logic, Paris, 1985 ⋮ Formalizing forcing arguments in subsystems of second-order arithmetic ⋮ On the arithmetical content of restricted forms of comprehension, choice and general uniform boundedness ⋮ The Baire category theorem in weak subsystems of second-order arithmetic ⋮ Saturated models of universal theories ⋮ THE PREHISTORY OF THE SUBSYSTEMS OF SECOND-ORDER ARITHMETIC

Cites Work

• Iterated inductive definitions and subsystems of analysis: recent proof-theoretical studies
• Metamathematical investigation of intuitionistic arithmetic and analysis. With contributions by C. A. Smorynski, J. I. Zucker and W. A. Howard
• Quantifier-free and one-quantifier systems
• Choice principles, the bar rule and autonomously iterated comprehension schemes in analysis
• The optimality of induction as an axiomatization of arithmetic
• Note on the fan theorem
• Systems of predicative analysis
• A survey of proof theory
• Grundlagen der Mathematik I
• On n-quantifier induction
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