Understanding uniformity in Feferman's explicit mathematics

Annals of Pure and Applied Logic 75 (1-2):89-106 (1995)

Abstract
The aim of this paper is the analysis of uniformity in Feferman's explicit mathematics. The proof-strength of those systems for constructive mathematics is determined by reductions to subsystems of second-order arithmetic: If uniformity is absent, the method of standard structures yields that the strength of the join axiom collapses. Systems with uniformity and join are treated via cut elimination and asymmetrical interpretations in standard structures.
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DOI 10.1016/0168-0072(94)00058-b
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References found in this work BETA

Proof Theory.Gaisi Takeuti - 1987 - Elsevier.
Proof Theory.K. Schütte - 1977 - Springer Verlag.
Partial Realizations of Hilbert's Program.Stephen G. Simpson - 1988 - Journal of Symbolic Logic 53 (2):349-363.

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Citations of this work BETA

On Power Set in Explicit Mathematics.Thomas Glass - 1996 - Journal of Symbolic Logic 61 (2):468-489.
Universes Over Frege Structures.Reinhard Kahle - 2003 - Annals of Pure and Applied Logic 119 (1-3):191-223.
A Theory of Rules for Enumerated Classes of Functions.Andreas Schlüter - 1995 - Archive for Mathematical Logic 34 (1):47-63.

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