Archive for Mathematical Logic 37 (5):391-413 (1998)

Abstract
. This paper is about two topics: 1. systems of explicit mathematics with universes and a non-constructive quantification operator $\mu$; 2. iterated fixed point theories with ordinals. We give a proof-theoretic treatment of both families of theories; in particular, ordinal theories are used to get upper bounds for explicit theories with finitely many universes.
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DOI 10.1007/s001530050105
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Universes in Explicit Mathematics.Gerhard Jäger, Reinhard Kahle & Thomas Studer - 2001 - Annals of Pure and Applied Logic 109 (3):141-162.
Universes Over Frege Structures.Reinhard Kahle - 2003 - Annals of Pure and Applied Logic 119 (1-3):191-223.

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