On power set in explicit mathematics

Journal of Symbolic Logic 61 (2):468-489 (1996)
This paper is concerned with the determination of the proof-strength of the power set axiom relative to axiom systems for Feferman's explicit mathematics. As conjectured by Feferman, we obtain that the presence of the power set axiom does not increase proof-strength. Results are achieved by reducing the systems including the power set axiom to subsystems of classical analysis. In those cases where only the induction axiom is available, we make use of the technique of asymmetrical interpretations
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DOI 10.2307/2275671
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The Strength of Some Martin-Löf Type Theories.Edward Griffor & Michael Rathjen - 1994 - Archive for Mathematical Logic 33 (5):347-385.

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The Universal Set and Diagonalization in Frege Structures.Reinhard Kahle - 2011 - Review of Symbolic Logic 4 (2):205-218.
Explicit Mathematics: Power Types and Overloading.Thomas Studer - 2005 - Annals of Pure and Applied Logic 134 (2-3):284-302.

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