Normalization of IZF with Replacement

  • Wojciech Moczydłowski
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4207)


IZF is a well investigated impredicative constructive version of Zermelo-Fraenkel set theory. Using set terms, we axiomatize IZF with Replacement, which we call IZF R , along with its intensional counterpart IZF\(_{R}^{\rm --}\) . We define a typed lambda calculus λZ corresponding to proofs in IZF\(_{R}^{\rm --}\) according to the Curry-Howard isomorphism principle. Using realizability for IZF\(_{R}^{\rm --}\) , we show weak normalization of λZ by employing a reduction-preserving erasure map from lambda terms to realizers. We use normalization to prove disjunction, numerical existence, set existence and term existence properties. An inner extensional model is used to show the properties for full, extensional IZF R .


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Wojciech Moczydłowski
    • 1
  1. 1.Department of Computer ScienceCornell UniversityIthacaUSA

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