{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,8,12]],"date-time":"2024-08-12T18:35:18Z","timestamp":1723487718735},"reference-count":32,"publisher":"Springer Science and Business Media LLC","issue":"7-8","license":[{"start":{"date-parts":[[2018,1,27]],"date-time":"2018-01-27T00:00:00Z","timestamp":1517011200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2018,1,27]],"date-time":"2018-01-27T00:00:00Z","timestamp":1517011200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001691","name":"Japan Society for the Promotion of Science","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100001691","id-type":"DOI","asserted-by":"publisher"}]},{"name":"GNSAGA-INDAM","award":["CPDA157295"]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Arch. Math. Logic"],"published-print":{"date-parts":[[2018,11]]},"DOI":"10.1007\/s00153-018-0612-9","type":"journal-article","created":{"date-parts":[[2018,1,27]],"date-time":"2018-01-27T07:44:18Z","timestamp":1517039058000},"page":"873-888","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Consistency of the intensional level of the Minimalist Foundation with Church\u2019s thesis and axiom of choice"],"prefix":"10.1007","volume":"57","author":[{"given":"Hajime","family":"Ishihara","sequence":"first","affiliation":[]},{"given":"Maria Emilia","family":"Maietti","sequence":"additional","affiliation":[]},{"given":"Samuele","family":"Maschio","sequence":"additional","affiliation":[]},{"given":"Thomas","family":"Streicher","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2018,1,27]]},"reference":[{"key":"612_CR1","unstructured":"Aczel, P.: The strength of Martin-L\u00f6f\u2019s intuitionistic type theory with one universe. In: Mietti, S., Vaananen, S. (eds.) Proceedings of Symposia in Mathematical Logic, Oulu, 1974, and Helsinki, 1975, Report No. 2, University of Helsinki, Department of philosophy, pp. 1\u201332 (1977)"},{"key":"612_CR2","doi-asserted-by":"crossref","unstructured":"Aczel, P.: The type theoretic interpretation of constructive set theory. In: Logic Colloquium \u201977 (Proceedings Conference, Wroc\u0142aw, 1977). Studies in Logic and the Foundations of Mathematics, vol.\u00a096. North-Holland, Amsterdam (1978)","DOI":"10.1016\/S0049-237X(08)71989-X"},{"key":"612_CR3","doi-asserted-by":"crossref","unstructured":"Aczel, P.: The type theoretic interpretation of constructive set theory: choice principles. In: Anne\u00a0Troelstra, D.D. (ed.) The L.E.J. Brouwer Centenary Symposium (Noordwijkerhout, 1981). Studies in Logic and the Foundations of Mathematics, vol.\u00a0110. North-Holland, Amsterdam (1982)","DOI":"10.1016\/S0049-237X(09)70120-X"},{"key":"612_CR4","doi-asserted-by":"crossref","unstructured":"Aczel, P.: The type theoretic interpretation of constructive set theory: inductive definitions. In: Logic, Methodology and Philosophy of Science, VII (Salzburg, 1983). Studies in Logic and the Foundations of Mathematics, vol.\u00a0114. North-Holland, Amsterdam (1986)","DOI":"10.1016\/S0049-237X(09)70683-4"},{"key":"612_CR5","unstructured":"Aczel, P., Rathjen, M.: Notes on constructive set theory. Mittag-Leffler technical report no. 40 (2001)"},{"issue":"2","key":"612_CR6","doi-asserted-by":"crossref","first-page":"261","DOI":"10.1017\/S0956796802004501","volume":"13","author":"G Barthes","year":"2003","unstructured":"Barthes, G., Capretta, V., Pons, O.: Setoids in type theory. J. Funct. Program. 13(2), 261\u2013293 (2003). (Special issue on \u201cLogical frameworks and metalanguages\u201d)","journal-title":"J. Funct. Program."},{"key":"612_CR7","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-68952-9","volume-title":"Foundations of Constructive Mathematics","author":"M Beeson","year":"1985","unstructured":"Beeson, M.: Foundations of Constructive Mathematics. Springer, Berlin (1985)"},{"key":"612_CR8","volume-title":"Foundations of Constructive Analysis","author":"E Bishop","year":"1967","unstructured":"Bishop, E.: Foundations of Constructive Analysis. McGraw-Hill Book Co., New York City (1967)"},{"key":"612_CR9","first-page":"91","volume-title":"Logic in Computer Science","author":"T Coquand","year":"1990","unstructured":"Coquand, T.: Metamathematical investigation of a calculus of constructions. In: Odifreddi, P. (ed.) Logic in Computer Science, pp. 91\u2013122. Academic Press, Cambridge (1990)"},{"key":"612_CR10","doi-asserted-by":"crossref","unstructured":"Coquand, T., Paulin-Mohring, C.: Inductively defined types. In: Martin-L\u00f6f, P., Mints, G. (eds.) Proceedings of the International Conference on Computer Logic (Colog \u201988). Lecture Notes in Computer Science, vol. 417, pp. 50\u201366. Springer, Berlin (1990)","DOI":"10.1007\/3-540-52335-9_47"},{"key":"612_CR11","doi-asserted-by":"crossref","unstructured":"Feferman, S.: Constructive theories of functions and classes. In: Boffa, M. et\u00a0al. (ed.) Logic Colloquium \u201978, pp. 159\u2013224. North-Holland (1979)","DOI":"10.1016\/S0049-237X(08)71625-2"},{"key":"612_CR12","doi-asserted-by":"crossref","unstructured":"Feferman, S.: Iterated inductive fixed-point theories: application to Hancock\u2019s conjecture. In: Patras Logic Symposium, pp. 171\u2013196. North Holland (1982)","DOI":"10.1016\/S0049-237X(08)71364-8"},{"key":"612_CR13","doi-asserted-by":"crossref","unstructured":"Hofmann, M.: Extensional constructs in intensional type theory. Distinguished Dissertations. Springer, London (1997)","DOI":"10.1007\/978-1-4471-0963-1"},{"key":"612_CR14","doi-asserted-by":"crossref","unstructured":"Hyland, J.M.E.: The effective topos. In: The L.E.J. Brouwer Centenary Symposium (Noordwijkerhout, 1981). Studies in Logic and the Foundations of Mathematics, vol. 110, pp. 165\u2013216. North-Holland, Amsterdam (1982)","DOI":"10.1016\/S0049-237X(09)70129-6"},{"key":"612_CR15","first-page":"205","volume":"88","author":"JME Hyland","year":"1980","unstructured":"Hyland, J.M.E., Johnstone, P.T., Pitts, A.M.: Tripos theory. Bull. Austral. Math. Soc. 88, 205\u2013232 (1980)","journal-title":"Bull. Austral. Math. Soc."},{"key":"612_CR16","series-title":"Lecture Note Series","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511752483","volume-title":"Algebraic Set Theory","author":"A Joyal","year":"1995","unstructured":"Joyal, A., Moerdijk, I.: Algebraic Set Theory. Lecture Note Series, vol. 220. Cambridge University Press, Cambridge (1995)"},{"key":"612_CR17","volume-title":"Sheaves in Geometry and Logic. A First Introduction to Topos Theory","author":"S MacLane","year":"1992","unstructured":"MacLane, S., Moerdijk, I.: Sheaves in Geometry and Logic. A First Introduction to Topos Theory. Springer, Berlin (1992)"},{"issue":"6","key":"612_CR18","doi-asserted-by":"publisher","first-page":"1089","DOI":"10.1017\/S0960129505004962","volume":"15","author":"M Maietti","year":"2005","unstructured":"Maietti, M.: Modular correspondence between dependent type theories and categories including pretopoi and topoi. Math. Struct. Comput. Sci. 15(6), 1089\u20131149 (2005)","journal-title":"Math. Struct. Comput. Sci."},{"issue":"3","key":"612_CR19","doi-asserted-by":"publisher","first-page":"319","DOI":"10.1016\/j.apal.2009.01.006","volume":"160","author":"ME Maietti","year":"2009","unstructured":"Maietti, M.E.: A minimalist two-level foundation for constructive mathematics. Ann. Pure Appl. Log. 160(3), 319\u2013354 (2009)","journal-title":"Ann. Pure Appl. Log."},{"issue":"17","key":"612_CR20","first-page":"445","volume":"27","author":"ME Maietti","year":"2013","unstructured":"Maietti, M.E., Rosolini, G.: Elementary quotient completion. Theory Appl. Categ. 27(17), 445\u2013463 (2013)","journal-title":"Theory Appl. Categ."},{"issue":"3","key":"612_CR21","doi-asserted-by":"publisher","first-page":"371","DOI":"10.1007\/s11787-013-0080-2","volume":"7","author":"ME Maietti","year":"2013","unstructured":"Maietti, M.E., Rosolini, G.: Quotient completion for the foundation of constructive mathematics. Log. Univer. 7(3), 371\u2013402 (2013)","journal-title":"Log. Univer."},{"key":"612_CR22","doi-asserted-by":"publisher","first-page":"43","DOI":"10.1007\/s10485-013-9360-5","volume":"23","author":"ME Maietti","year":"2015","unstructured":"Maietti, M.E., Rosolini, G.: Unifying exact completions. Appl. Categ. Struct. 23, 43\u201352 (2015)","journal-title":"Appl. Categ. Struct."},{"key":"612_CR23","series-title":"Oxford Logic Guides","doi-asserted-by":"publisher","first-page":"91","DOI":"10.1093\/acprof:oso\/9780198566519.003.0006","volume-title":"From Sets and Types to Topology and Analysis: Practicable Foundations for Constructive Mathematics","author":"ME Maietti","year":"2005","unstructured":"Maietti, M.E., Sambin, G.: Toward a minimalist foundation for constructive mathematics. In: Crosilla, L., Schuster, P. (eds.) From Sets and Types to Topology and Analysis: Practicable Foundations for Constructive Mathematics. Oxford Logic Guides, vol. 48, pp. 91\u2013114. Oxford University Press, Oxford (2005)"},{"issue":"2","key":"612_CR24","first-page":"167","volume":"22","author":"ME Maietti","year":"2013","unstructured":"Maietti, M.E., Sambin, G.: Why topology in the minimalist foundation must be pointfree. Log. Log. Philos. 22(2), 167\u2013199 (2013)","journal-title":"Log. Log. Philos."},{"key":"612_CR25","series-title":"Notes by G. Sambin of a Series of Lectures Given in Padua, June 1980","volume-title":"Intuitionistic Type Theory","author":"P Martin-L\u00f6f","year":"1984","unstructured":"Martin-L\u00f6f, P.: Intuitionistic Type Theory. Notes by G. Sambin of a Series of Lectures Given in Padua, June 1980. Bibliopolis, Naples (1984)"},{"key":"612_CR26","volume-title":"Programming in Martin L\u00f6f\u2019s Type Theory","author":"B Nordstr\u00f6m","year":"1990","unstructured":"Nordstr\u00f6m, B., Petersson, K., Smith, J.: Programming in Martin L\u00f6f\u2019s Type Theory. Clarendon Press, Oxford (1990)"},{"key":"612_CR27","series-title":"Studies in Logic and the Foundations of Mathematics","volume-title":"Classical Recursion Theory","author":"P Odifreddi","year":"1989","unstructured":"Odifreddi, P.: Classical Recursion Theory. Studies in Logic and the Foundations of Mathematics, vol. 125. North-Holland Publishing Co., Amsterdam (1989)"},{"key":"612_CR28","unstructured":"Palmgren, E.: Bishop\u2019s set theory. In: Slides for Lecture at the TYPES Summer School (2005)"},{"issue":"2","key":"612_CR29","doi-asserted-by":"publisher","first-page":"395","DOI":"10.1016\/0304-3975(92)90021-7","volume":"103","author":"T Streicher","year":"1992","unstructured":"Streicher, T.: Independence of the induction principle and the axiom of choice in the pure calculus of constructions. Theor. Comput. Sci. 103(2), 395\u2013408 (1992)","journal-title":"Theor. Comput. Sci."},{"key":"612_CR30","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0066739","volume-title":"Metamathematical Investigation of Intuitionistic Arithmetic and Analysis","author":"AS Troelstra","year":"1973","unstructured":"Troelstra, A.S.: Metamathematical Investigation of Intuitionistic Arithmetic and Analysis. Springer, Berlin (1973)"},{"key":"612_CR31","series-title":"Studies in Logic and the Foundations of Mathematics","volume-title":"Constructivism in Mathematics: An Introduction","author":"AS Troelstra","year":"1988","unstructured":"Troelstra, A.S., van Dalen, D.: Constructivism in Mathematics: An Introduction. Studies in Logic and the Foundations of Mathematics, vol. I and II. North-Holland, Amsterdam (1988)"},{"key":"612_CR32","series-title":"Studies in Logic and the Foundations of Mathematics","volume-title":"Realizability: An Introduction to Its Categorical Side","author":"J van Oosten","year":"2008","unstructured":"van Oosten, J.: Realizability: An Introduction to Its Categorical Side. Studies in Logic and the Foundations of Mathematics, vol. 152. Elsevier, Amsterdam (2008)"}],"container-title":["Archive for Mathematical Logic"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00153-018-0612-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00153-018-0612-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00153-018-0612-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,5,15]],"date-time":"2020-05-15T18:31:46Z","timestamp":1589567506000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00153-018-0612-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,1,27]]},"references-count":32,"journal-issue":{"issue":"7-8","published-print":{"date-parts":[[2018,11]]}},"alternative-id":["612"],"URL":"https:\/\/doi.org\/10.1007\/s00153-018-0612-9","relation":{},"ISSN":["0933-5846","1432-0665"],"issn-type":[{"value":"0933-5846","type":"print"},{"value":"1432-0665","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,1,27]]},"assertion":[{"value":"31 January 2017","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"18 January 2018","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 January 2018","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}