## Moczydlowski, Wojciech - Normalization of IZF with Replacement

lmcs:1235 - Logical Methods in Computer Science, April 8, 2008, Volume 4, Issue 2
Normalization of IZF with Replacement

Authors: Moczydlowski, Wojciech

ZF is a well investigated impredicative constructive version of Zermelo-Fraenkel set theory. Using set terms, we axiomatize IZF with Replacement, which we call \izfr, along with its intensional counterpart \iizfr. We define a typed lambda calculus $\li$ corresponding to proofs in \iizfr according to the Curry-Howard isomorphism principle. Using realizability for \iizfr, we show weak normalization of $\li$. We use normalization to prove the disjunction, numerical existence and term existence properties. An inner extensional model is used to show these properties, along with the set existence property, for full, extensional \izfr.

Source : oai:arXiv.org:0711.2546
DOI : 10.2168/LMCS-4(2:1)2008
Volume: Volume 4, Issue 2
Published on: April 8, 2008
Submitted on: January 2, 2007
Keywords: Computer Science - Logic in Computer Science,F.4.1