Systems of explicit mathematics with non-constructive μ-operator. Part I

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Annals of Pure and Applied Logic 65 (3):243-263 (1993)
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Abstract

Feferman, S. and G. Jäger, Systems of explicit mathematics with non-constructive μ-operator. Part I, Annals of Pure and Applied Logic 65 243-263. This paper is mainly concerned with the proof-theoretic analysis of systems of explicit mathematics with a non-constructive minimum operator. We start off from a basic theory BON of operators and numbers and add some principles of set and formula induction on the natural numbers as well as axioms for μ. The principal results then state: BON plus set induction is proof-theoretically equivalent to Peano arithmetic PA; BON plus formula induction is proof-theoretically equivalent to the system <0 of second-order arithmetic

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10.1016/0168-0072(93)90013-4

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Citations of this work

The unfolding of non-finitist arithmetic.Solomon Feferman & Thomas Strahm - 2000 - Annals of Pure and Applied Logic 104 (1-3):75-96.
On Feferman’s operational set theory OST.Gerhard Jäger - 2007 - Annals of Pure and Applied Logic 150 (1-3):19-39.
Totality in applicative theories.Gerhard Jäger & Thomas Strahm - 1995 - Annals of Pure and Applied Logic 74 (2):105-120.

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References found in this work

A well-ordering proof for Feferman's theoryT 0.Gerhard Jäger - 1983 - Archive for Mathematical Logic 23 (1):65-77.
Fixed points in Peano arithmetic with ordinals.Gerhard Jäger - 1993 - Annals of Pure and Applied Logic 60 (2):119-132.

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