Systems of Explicit Mathematics with Non-Constructive µ-Operator, Part I

Feferman, S. and G. Jager, Systems of explicit mathematics with non-constructive μ-operator. Part I, Annals of Pure and Applied Logic 65 (1993) 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: (i) BON(μ) plus set induction is proof-theoretically equivalent to Peano arithmetic PA; (ii) BON(μ) plus formula induction is proof-theoretically equivalent to the system (Π0∞-CA)

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