Realization of constructive set theory into explicit mathematics: a lower bound for impredicative Mahlo universe

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Abstract

We define a realizability interpretation of Aczel's Constructive Set Theory CZF into Explicit Mathematics. The final results are that CZF extended by Mahlo principles is realizable in corresponding extensions of T0, thus providing relative lower bounds for the proof-theoretic strength of the latter.

MSC

03F25
03F55
03F65

Keywords

Explicit Mathematics, Constructive Set Theory
Realizability

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In the Russian language the word “malo” means “a little”, “not enough”.

1

Research supported by the Swiss National Science Foundation. This paper was completed during the author's appointment at the Institute for Informatics and Applied Mathematics, University of Bern, Switzerland, in 1998–2000, and is an updated version of the technical report [28].