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

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Annals of Pure and Applied Logic 79 (1):37-52 (1996)
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Abstract

This paper is mainly concerned with proof-theoretic analysis of some second-order systems of explicit mathematics with a non-constructive minimum operator. By introducing axioms for variable types we extend our first-order theory BON to the elementary explicit type theory EET and add several forms of induction as well as axioms for μ. The principal results then state: EET plus set induction is proof-theoretically equivalent to Peano arithmetic PA <0)

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10.1016/0168-0072(95)00028-3

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Citations of this work

Hilbert’s Program.Richard Zach - 2014 - In Edward N. Zalta (ed.), The Stanford Encyclopedia of Philosophy. Stanford, CA: The Metaphysics Research Lab.
Why a Little Bit Goes a Long Way: Logical Foundations of Scientifically Applicable Mathematics.Solomon Feferman - 1992 - PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1992:442 - 455.
The unfolding of non-finitist arithmetic.Solomon Feferman & Thomas Strahm - 2000 - Annals of Pure and Applied Logic 104 (1-3):75-96.

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Totality in applicative theories.Gerhard Jäger & Thomas Strahm - 1995 - Annals of Pure and Applied Logic 74 (2):105-120.

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