{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,25]],"date-time":"2025-03-25T15:57:52Z","timestamp":1742918272220,"version":"3.40.3"},"publisher-location":"Berlin, Heidelberg","reference-count":26,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783642390524"},{"type":"electronic","value":"9783642390531"}],"license":[{"start":{"date-parts":[[2013,1,1]],"date-time":"2013-01-01T00:00:00Z","timestamp":1356998400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2013,1,1]],"date-time":"2013-01-01T00:00:00Z","timestamp":1356998400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2013]]},"DOI":"10.1007\/978-3-642-39053-1_35","type":"book-chapter","created":{"date-parts":[[2013,6,3]],"date-time":"2013-06-03T04:28:12Z","timestamp":1370233692000},"page":"306-315","source":"Crossref","is-referenced-by-count":0,"title":["Realizability Models Separating Various Fan Theorems"],"prefix":"10.1007","author":[{"given":"Robert S.","family":"Lubarsky","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Michael","family":"Rathjen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"issue":"3","key":"35_CR1","doi-asserted-by":"publisher","first-page":"215","DOI":"10.1016\/S0022-4049(02)00283-9","volume":"177","author":"S. Awodey","year":"2003","unstructured":"Awodey, S., Birkedal, L.: Elementary axioms for local maps of toposes. Journal of Pure and Applied Algebra\u00a0177(3), 215\u2013230 (2003)","journal-title":"Journal of Pure and Applied Algebra"},{"key":"35_CR2","unstructured":"Bauer, A.: The Realizability approach to computable analysis and topology. Ph.D. Thesis (2000)"},{"key":"35_CR3","doi-asserted-by":"crossref","unstructured":"Beeson, M.: Foundations of Constructive Mathematics. Springer (1985)","DOI":"10.1007\/978-3-642-68952-9"},{"key":"35_CR4","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"35","DOI":"10.1007\/11780342_4","volume-title":"Logical Approaches to Computational Barriers","author":"J. Berger","year":"2006","unstructured":"Berger, J.: The Logical strength of the uniform continuity theorem. In: Beckmann, A., Berger, U., L\u00f6we, B., Tucker, J.V. (eds.) CiE 2006. LNCS, vol.\u00a03988, pp. 35\u201339. Springer, Heidelberg (2006)"},{"issue":"6","key":"35_CR5","first-page":"1","volume":"1","author":"J. Berger","year":"2009","unstructured":"Berger, J.: A decomposition of Brouwers fan theorem. Journal of Logic and Analysis\u00a01(6), 1\u20138 (2009)","journal-title":"Journal of Logic and Analysis"},{"key":"35_CR6","volume-title":"Proceedings of the 10th Asian Logic Conference (alc 10)","author":"J. Berger","year":"2008","unstructured":"Berger, J.: A separation result for varieties of Brouwer\u2019s fan theorem. In: Proceedings of the 10th Asian Logic Conference (alc 10), September 1-6, Kobe University in Kobe, hyogo (2008); Arai, et al (eds.) World Scientific, pp.85\u201392 (2010)"},{"issue":"4","key":"35_CR7","doi-asserted-by":"publisher","first-page":"360","DOI":"10.1002\/malq.200410038","volume":"51","author":"J. Berger","year":"2005","unstructured":"Berger, J., Ishihara, H.: Brouwers fan theorem and unique existence in constructive analysis. Mathematical Logic Quarterly\u00a051(4), 360\u2013364 (2005), doi:10.1002\/malq.200410038","journal-title":"Mathematical Logic Quarterly"},{"issue":"1-2","key":"35_CR8","doi-asserted-by":"publisher","first-page":"115","DOI":"10.1016\/S0168-0072(01)00122-1","volume":"118","author":"L. Birkedal","year":"2002","unstructured":"Birkedal, L., van Oosten, J.: Relative and modified relative realizability. Annals of Pure and Applied Logic\u00a0118(1-2), 115\u2013132 (2002)","journal-title":"Annals of Pure and Applied Logic"},{"key":"35_CR9","doi-asserted-by":"crossref","unstructured":"Bishop, E., Bridges, D.: Constructive Analysis. Springer (1985)","DOI":"10.1007\/978-3-642-61667-9"},{"key":"35_CR10","unstructured":"de Jongh, D.H.J.: The Maximality of the intuitionistic predicate calculus with respect to Heyting\u2019s Arithmetic. Typed manuscript (1969)"},{"key":"35_CR11","unstructured":"Diener, H.: Compactness under constructive scrutiny. Ph.D. Thesis (2008)"},{"issue":"1","key":"35_CR12","doi-asserted-by":"publisher","first-page":"50","DOI":"10.1016\/j.apal.2008.09.018","volume":"157","author":"H. Diener","year":"2009","unstructured":"Diener, H., Loeb, I.: Sequences of real functions on [0, 1] in constructive reverse mathematics. Annals of Pure and Applied Logic\u00a0157(1), 50\u201361 (2009)","journal-title":"Annals of Pure and Applied Logic"},{"key":"35_CR13","series-title":"Lecture Notes in Mathematics","doi-asserted-by":"publisher","first-page":"280","DOI":"10.1007\/BFb0061823","volume-title":"Applications of Sheaves","author":"M. Fourman","year":"1979","unstructured":"Fourman, M., Hyland, J.M.E.: Sheaf models for analysis. In: Fourman, M., Mulvey, C., Scott, D. (eds.) Applications of Sheaves. Lecture Notes in Mathematics, vol.\u00a0753, pp. 280\u2013301. Springer, Heidelberg (1979), http:\/\/dx.doi.org\/10.1007\/BFb0061823"},{"key":"35_CR14","doi-asserted-by":"publisher","first-page":"23","DOI":"10.2307\/2271946","volume":"43","author":"N.D. Goodman","year":"1978","unstructured":"Goodman, N.D.: Relativized realizability in intuitionistic arithmetic of all finite types. Journal of Symbolic Logic\u00a043, 23\u201344 (1978)","journal-title":"Journal of Symbolic Logic"},{"issue":"2","key":"35_CR15","doi-asserted-by":"publisher","first-page":"333","DOI":"10.2140\/pjm.1984.111.333","volume":"111","author":"W. Julian","year":"1984","unstructured":"Julian, W., Richman, F.: A Uniformly continuous function on [0,1] that is everywhere different from its infimum. Pacific Journal of Mathematics\u00a0111(2), 333\u2013340 (1984)","journal-title":"Pacific Journal of Mathematics"},{"key":"35_CR16","unstructured":"Kleene, S.C., Vesley, R.E.: The Foundations of Intuitionistic Mathematics. North-Holland (1965)"},{"issue":"2-3","key":"35_CR17","doi-asserted-by":"publisher","first-page":"209","DOI":"10.1016\/j.apal.2004.08.002","volume":"132","author":"R. Lubarsky","year":"2005","unstructured":"Lubarsky, R.: Independence results around Constructive ZF. Annals of Pure and Applied Logic\u00a0132(2-3), 209\u2013225 (2005)","journal-title":"Annals of Pure and Applied Logic"},{"key":"35_CR18","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"280","DOI":"10.1007\/978-3-642-35722-0_20","volume-title":"Logical Foundations of Computer Science","author":"R.S. Lubarsky","year":"2013","unstructured":"Lubarsky, R.S., Diener, H.: Separating the Fan Theorem and Its Weakenings. In: Artemov, S., Nerode, A. (eds.) LFCS 2013. LNCS, vol.\u00a07734, pp. 280\u2013295. Springer, Heidelberg (2013)"},{"key":"35_CR19","doi-asserted-by":"crossref","unstructured":"Moschovakis, J.: Another Unique Weak K\u00f6nig\u2019s Lemma. In: Berger, U., Diener, H., Schuster, P., Seisenberger, M. (eds.) Logic, Construction, Computation, Ontos (to appear, 2013)","DOI":"10.1515\/9783110324921.343"},{"key":"35_CR20","doi-asserted-by":"crossref","unstructured":"Nemoto, T.: Weak weak K\u00f6nig\u2019s Lemma in constructive reverse mathematics. In: Proceedings of the 10th Asian Logic Conference (alc 10), September 1-6, Kobe University in Kobe, hyogo (2008) Arai, et al (eds) World Scientific, pp. 263\u2013270 (2010)","DOI":"10.1142\/9789814293020_0010"},{"key":"35_CR21","first-page":"2008","volume":"11","author":"M. Rathjen","year":"2005","unstructured":"Rathjen, M.: Constructive Set Theory and Brouwerian Principles. Journal of Universal Computer Science\u00a011, 2008\u20132033 (2005)","journal-title":"Journal of Universal Computer Science"},{"key":"35_CR22","doi-asserted-by":"crossref","unstructured":"Simpson, S.: Subsystems of Second Order Arithmetic. ASL\/Cambridge University Press (2009)","DOI":"10.1017\/CBO9780511581007"},{"key":"35_CR23","unstructured":"Troelstra, A.S., van Dalen, D.: Constructivism in Mathematics, vol.\u00a01. North-Holland (1988)"},{"key":"35_CR24","doi-asserted-by":"publisher","first-page":"105","DOI":"10.1007\/BF01387763","volume":"31","author":"J. van Oosten","year":"1991","unstructured":"van Oosten, J.: A Semantical proof of De Jongh\u2019s theorem. Archive for Mathematical Logic\u00a031, 105\u2013114 (1991)","journal-title":"Archive for Mathematical Logic"},{"key":"35_CR25","unstructured":"van Oosten, J.: Realizability: An Introduction to its Categorical Side. Elsevier (2008)"},{"key":"35_CR26","doi-asserted-by":"publisher","first-page":"171","DOI":"10.1007\/BF01621469","volume":"30","author":"X. Yu","year":"1990","unstructured":"Yu, X., Simpson, S.: Measure theory and weak K\u00f6nigs lemma. Archive for Mathematical Logic\u00a030, 171\u2013180 (1990)","journal-title":"Archive for Mathematical Logic"}],"container-title":["Lecture Notes in Computer Science","The Nature of Computation. Logic, Algorithms, Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-642-39053-1_35","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,7,2]],"date-time":"2023-07-02T03:58:17Z","timestamp":1688270297000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-642-39053-1_35"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013]]},"ISBN":["9783642390524","9783642390531"],"references-count":26,"URL":"https:\/\/doi.org\/10.1007\/978-3-642-39053-1_35","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2013]]}}}