Fragments of Arithmetic and true sentences

DOI10.1002/malq.200410034zbMath1067.03064OpenAlexW1517203860MaRDI QIDQ4680381

A. Fernández-Margarit, Andrés Cordón-Franco, F. F. Lara-Martín

Publication date: 1 June 2005

Published in: Mathematical Logic Quarterly (Search for Journal in Brave)

Full work available at URL: https://idus.us.es/handle//11441/87545

zbMATH Keywords

quantifier complexityfragments of arithmetic\(\Delta_{n+1}\)-formulasparameter-free schemestrue sentences

Mathematics Subject Classification ID

First-order arithmetic and fragments (03F30) Nonstandard models of arithmetic (03H15) Models of arithmetic and set theory (03C62)

Related Items (5)

Semi-honest subrecursive degrees and the collection rule in arithmetic ⋮ PREDICATIVITY THROUGH TRANSFINITE REFLECTION ⋮ On axiom schemes for \(T\)-provably \(\Delta_1\) formulas ⋮ A note on Σ₁-maximal models ⋮ A note on parameter free Π₁ -induction and restricted exponentiation

Cites Work

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• Induction, minimization and collection for \(\Delta_{n+1}(T)\)-formulas
• On the scheme of induction for bounded arithmetic formulas
• Induction rules, reflection principles, and provably recursive functions
• Parameter free induction and provably total computable functions
• Some Results on LΔn+1
• The optimality of induction as an axiomatization of arithmetic
• On parameter free induction schemas
• On the induction schema for decidable predicates
• Σ_{𝑛}-bounding and Δ_{𝑛}-induction

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