{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T15:40:30Z","timestamp":1753890030849,"version":"3.41.2"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","license":[{"start":{"date-parts":[[2008,4,8]],"date-time":"2008-04-08T00:00:00Z","timestamp":1207612800000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/arxiv.org\/licenses\/assumed-1991-2003"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:p>ZF is a well investigated impredicative constructive version of\nZermelo-Fraenkel set theory. Using set terms, we axiomatize IZF with\nReplacement, which we call \\izfr, along with its intensional counterpart\n\\iizfr. We define a typed lambda calculus $\\li$ corresponding to proofs in\n\\iizfr according to the Curry-Howard isomorphism principle. Using realizability\nfor \\iizfr, we show weak normalization of $\\li$. We use normalization to prove\nthe disjunction, numerical existence and term existence properties. An inner\nextensional model is used to show these properties, along with the set\nexistence property, for full, extensional \\izfr.<\/jats:p>","DOI":"10.2168\/lmcs-4(2:1)2008","type":"journal-article","created":{"date-parts":[[2008,6,3]],"date-time":"2008-06-03T13:28:28Z","timestamp":1212499708000},"source":"Crossref","is-referenced-by-count":0,"title":["Normalization of IZF with Replacement"],"prefix":"10.46298","volume":"Volume 4, Issue 2","author":[{"given":"Wojciech","family":"Moczydlowski","sequence":"first","affiliation":[]}],"member":"25203","published-online":{"date-parts":[[2008,4,8]]},"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/lmcs.episciences.org\/1235\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/lmcs.episciences.org\/1235\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,4,11]],"date-time":"2023-04-11T20:06:18Z","timestamp":1681243578000},"score":1,"resource":{"primary":{"URL":"https:\/\/lmcs.episciences.org\/1235"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,4,8]]},"references-count":0,"URL":"https:\/\/doi.org\/10.2168\/lmcs-4(2:1)2008","relation":{"is-same-as":[{"id-type":"arxiv","id":"0711.2546","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.0711.2546","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"type":"electronic","value":"1860-5974"}],"subject":[],"published":{"date-parts":[[2008,4,8]]},"article-number":"1235"}}