The [mathematical formula] quantification operator in explicit mathematics with universes and iterated fixed point theories with ordinals

Archive for Mathematical Logic 36 (6):391-413 (1997)
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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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