On power set in explicit mathematics

Journal of Symbolic Logic 61 (2):468-489 (1996)
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Abstract

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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10.2307/2275671

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Citations of this work

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.
Relating Quine's NF to Feferman's EM.Andrea Cantini - 1999 - Studia Logica 62 (2):141-162.

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References found in this work

Subsystems of Second Order Arithmetic.Stephen G. Simpson - 1999 - Studia Logica 77 (1):129-129.
The strength of some Martin-Löf type theories.Edward Griffor & Michael Rathjen - 1994 - Archive for Mathematical Logic 33 (5):347-385.
Understanding uniformity in Feferman's explicit mathematics.Thomas Glaß - 1995 - Annals of Pure and Applied Logic 75 (1-2):89-106.
An extended Lachlan splitting theorem.Steffen Lempp & Sui Yuefei - 1996 - Annals of Pure and Applied Logic 79 (1):53-59.

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