Some theories with positive induction of ordinal strength ϕω

Journal of Symbolic Logic 61 (3):818-842 (1996)
Abstract
This paper deals with: (i) the theory ID # 1 which results from $\widehat{\mathrm{ID}}_1$ by restricting induction on the natural numbers to formulas which are positive in the fixed point constants, (ii) the theory BON(μ) plus various forms of positive induction, and (iii) a subtheory of Peano arithmetic with ordinals in which induction on the natural numbers is restricted to formulas which are Σ in the ordinals. We show that these systems have proof-theoretic strength φω 0
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DOI 10.2307/2275787
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References found in this work BETA
Andrea Cantini (1989). Notes on Formal Theories of Truth. Zeitshrift für Mathematische Logik Und Grundlagen der Mathematik 35 (1):97--130.
Wilfried Sieg (1985). Fragments of Arithmetic. Annals of Pure and Applied Logic 28 (1):33-71.
Gerhard Jäger (1993). Fixed Points in Peano Arithmetic with Ordinals. Annals of Pure and Applied Logic 60 (2):119-132.

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Citations of this work BETA
Reinhard Kahle (2003). Universes Over Frege Structures. Annals of Pure and Applied Logic 119 (1-3):191-223.

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