{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,30]],"date-time":"2025-10-30T18:36:34Z","timestamp":1761849394862,"version":"build-2065373602"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"accepted":{"date-parts":[[2025,8,12]]},"abstract":"<jats:p>Rathjen proved that Aczel's constructive set theory $\\mathbf{CZF}$ extended with inaccessible sets of all transfinite orders can be interpreted in Martin-L\u00f6f type theory $\\mathbf{MLTT}$ extended with Setzer's Mahlo universe and another universe above it. In this paper we show that this interpretation can be carried out bottom-up without the universe above the Mahlo universe, provided we add an accessibility predicate instead. If we work in Martin-L\u00f6f type theory with extensional identity types the accessibility predicate can be defined in terms of $\\mathrm{W}$-types. The main part of our interpretation has been formalised in the proof assistant Agda.<\/jats:p>","DOI":"10.46298\/lmcs-21(4:16)2025","type":"journal-article","created":{"date-parts":[[2025,10,30]],"date-time":"2025-10-30T18:15:08Z","timestamp":1761848108000},"source":"Crossref","is-referenced-by-count":0,"title":["Interpretation of Inaccessible Sets in Martin-L\u00f6f Type Theory with One Mahlo Universe"],"prefix":"10.46298","volume":"Volume 21, Issue 4","author":[{"given":"Yuta","family":"Takahashi","sequence":"first","affiliation":[]}],"member":"25203","published-online":{"date-parts":[[2025,10,30]]},"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/arxiv.org\/pdf\/2402.15074v5","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/arxiv.org\/pdf\/2402.15074v5","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,30]],"date-time":"2025-10-30T18:15:08Z","timestamp":1761848108000},"score":1,"resource":{"primary":{"URL":"https:\/\/lmcs.episciences.org\/13122"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,10,30]]},"references-count":0,"URL":"https:\/\/doi.org\/10.46298\/lmcs-21(4:16)2025","relation":{"has-preprint":[{"id-type":"arxiv","id":"2402.15074v3","asserted-by":"subject"},{"id-type":"arxiv","id":"2402.15074v2","asserted-by":"subject"},{"id-type":"arxiv","id":"2402.15074v1","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"2402.15074","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.2402.15074","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"value":"1860-5974","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,10,30]]},"article-number":"13122"}}