{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,25]],"date-time":"2026-03-25T10:55:30Z","timestamp":1774436130602,"version":"3.50.1"},"reference-count":32,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2020,6,19]],"date-time":"2020-06-19T00:00:00Z","timestamp":1592524800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,6,19]],"date-time":"2020-06-19T00:00:00Z","timestamp":1592524800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Order"],"published-print":{"date-parts":[[2021,4]]},"DOI":"10.1007\/s11083-020-09531-6","type":"journal-article","created":{"date-parts":[[2020,6,19]],"date-time":"2020-06-19T03:57:31Z","timestamp":1592539051000},"page":"111-125","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Topos Quantum Theory with Short Posets"],"prefix":"10.1007","volume":"38","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8539-0372","authenticated-orcid":false,"given":"John","family":"Harding","sequence":"first","affiliation":[]},{"given":"Chris","family":"Heunen","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2020,6,19]]},"reference":[{"key":"9531_CR1","doi-asserted-by":"publisher","first-page":"21","DOI":"10.4204\/EPTCS.236.2","volume":"236","author":"G Car\u00f9","year":"2017","unstructured":"Car\u00f9, G.: On the cohomology of contextuality. Proceedings of QPL, EPTCS 236, 21\u201339 (2017)","journal-title":"Proceedings of QPL, EPTCS"},{"issue":"2","key":"9531_CR2","first-page":"397","volume":"42","author":"C Constantin","year":"2016","unstructured":"Constantin, C., D\u00f6ring, A.: Reconstructing an atomic orthomodular lattice from the poset of its Boolean sublattices. Houston J. Math. 42(2), 397\u2013409 (2016)","journal-title":"Houston J. Math."},{"key":"9531_CR3","unstructured":"D\u00f6ring, A: Quantum states and measures on the spectral presheaf. arXiv:0809.4847 (2008)"},{"issue":"2047","key":"9531_CR4","first-page":"1","volume":"373","author":"A D\u00f6ring","year":"2015","unstructured":"D\u00f6ring, A.: Spectral presheaves as quantum state spaces. Philos. Trans. Roy. Soc. A 373(2047), 1\u201318 (2015)","journal-title":"Philos. Trans. Roy. Soc. A"},{"key":"9531_CR5","volume-title":"Topos-Based Logic for Quantum Systems and bi-Heyting Algebras, Logic and Algebraic Structures in Quantum Computing, 151-173, Lect Notes Log., 45","author":"A D\u00f6ring","year":"2016","unstructured":"D\u00f6ring, A.: Topos-Based Logic for Quantum Systems and bi-Heyting Algebras, Logic and Algebraic Structures in Quantum Computing, 151-173, Lect Notes Log., 45. Assoc. Symbol. Logic, La Jolla (2016)"},{"issue":"2","key":"9531_CR6","doi-asserted-by":"publisher","first-page":"499","DOI":"10.1007\/s00220-014-1991-3","volume":"328","author":"A D\u00f6ring","year":"2014","unstructured":"D\u00f6ring, A., Dewitt, B.: Self-adjoint operators as functions I. Comm. Math. Phys. 328(2), 499\u2013525 (2014)","journal-title":"Comm. Math. Phys."},{"issue":"2","key":"9531_CR7","first-page":"559","volume":"42","author":"A D\u00f6ring","year":"2016","unstructured":"D\u00f6ring, A., Harding, J.: Abelian subalgebras and the Jordan structure of a von Neumann algebra. Houston J. Math. 42(2), 559\u2013568 (2016)","journal-title":"Houston J. Math."},{"key":"9531_CR8","unstructured":"D\u00f6ring, A., Isham, C.J.: \u2018What is a thing?\u2019:, topos theory in the foundations of physics. arXiv:0803.0417 (2008)"},{"key":"9531_CR9","volume-title":"\u2018What is a Thing?\u2019: Topos Theory in the Foundations of Physics, New structures for physics, 753-937, Lecture Notes in Phys. 813","author":"A D\u00f6ring","year":"2011","unstructured":"D\u00f6ring, A., Isham, C.J.: \u2018What is a Thing?\u2019: Topos Theory in the Foundations of Physics, New structures for physics, 753-937, Lecture Notes in Phys. 813. Springer, Heidelberg (2011)"},{"issue":"3","key":"9531_CR10","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1063\/1.3688627","volume":"53","author":"AA D\u00f6ring","year":"2012","unstructured":"D\u00f6ring, A.A., Isham, C.J.: Classical and quantum probabilities as truth values. J. Math. Phys. 53(3), 1\u201326 (2012)","journal-title":"J. Math. Phys."},{"key":"9531_CR11","unstructured":"D\u00f6ring, A.: Generalized Gelfand spectra arXiv:1212.2613v2 (2013)"},{"key":"9531_CR12","unstructured":"Doring, A.: Flows on generalized Gelfand spectra of nonabelian unital c\u2217-algebras and time evolution of quantum systems, arXiv:1212.4882v2 (2013)"},{"key":"9531_CR13","volume-title":"Modern Projective Geometry Mathematics and Its Applications, vol. 521","author":"C Faure","year":"2000","unstructured":"Faure, C., Fr\u00f6licher, A.: Modern Projective Geometry Mathematics and Its Applications, vol. 521. Kluwer Academic Publishers, Dordrecht (2000)"},{"key":"9531_CR14","unstructured":"Flori, C.: Review of the topos approach to quantum theory. arXiv:1106.5660 (2011)"},{"key":"9531_CR15","doi-asserted-by":"crossref","unstructured":"Flori, C.: A first course in topos quantum theory, Lecture Notes in Physics 868, Springer-Verlag (2013)","DOI":"10.1007\/978-3-642-35713-8"},{"key":"9531_CR16","doi-asserted-by":"crossref","unstructured":"Flori, C.: A second course in topos quantum theory, Lecture Notes in Physics 944, Springer-Verlag (2018)","DOI":"10.1007\/978-3-319-71108-9"},{"key":"9531_CR17","doi-asserted-by":"crossref","unstructured":"Harding, J., Heunen, C., Lindenhovius, A.J., Navara, M.: Boolean subalgebras of orthoalgebras. arXiv:1711.03748 (2018)","DOI":"10.1007\/s11083-019-09483-6"},{"key":"9531_CR18","doi-asserted-by":"publisher","first-page":"539","DOI":"10.1007\/s10773-005-3981-x","volume":"44","author":"J Harding","year":"2005","unstructured":"Harding, J., Jager, E., Smith, D.: Group-valued measures on the lattice of closed subspaces of a Hilbert space. Internat. J. Theoret. Phys. 44, 539\u2013548 (2005)","journal-title":"Internat. J. Theoret. Phys."},{"key":"9531_CR19","unstructured":"Harding, J., Lindenhovius, A.J.: Hypergraphs and AW*-algebras, manuscript"},{"key":"9531_CR20","doi-asserted-by":"publisher","first-page":"144","DOI":"10.3390\/e19040144","volume":"19","author":"C Heunen","year":"2017","unstructured":"Heunen, C.: The many classical faces of quantum structures. Entropy 19, 144 (2017)","journal-title":"Entropy"},{"key":"9531_CR21","doi-asserted-by":"publisher","first-page":"63","DOI":"10.1007\/s00220-009-0865-6","volume":"291","author":"C Heunen","year":"2009","unstructured":"Heunen, C., Landsman, N.P., Spitters, B.: A topos for algebraic quantum theory. Commun. Math. Phys. 291, 63\u2013110 (2009)","journal-title":"Commun. Math. Phys."},{"key":"9531_CR22","doi-asserted-by":"publisher","unstructured":"Heunen, C., Landsman, N.P., Spitters, B.: Bohrification of Operator Algebras and Quantum Logic, Synthese. https:\/\/doi.org\/10.1007\/s11229-011-9918-4 (2011)","DOI":"10.1007\/s11229-011-9918-4"},{"key":"9531_CR23","doi-asserted-by":"crossref","unstructured":"Heunen, C., Landsman, N.P., Spitters, B.: Bohrification. Deep beauty: Mathematical Innovation and Research for Underlying Intelligibility in the Quantum world, ed. Hans Halvorson Cambridge University Press (2011)","DOI":"10.1017\/CBO9780511976971.008"},{"key":"9531_CR24","first-page":"67","volume":"5","author":"T Hosoi","year":"1973","unstructured":"Hosoi, T., Ono, H.: Intermediate propositional logics (a survey). Tsudajuku Daigaku kiy\u00f5 5, 67\u201382 (1973)","journal-title":"Tsudajuku Daigaku kiy\u00f5"},{"key":"9531_CR25","doi-asserted-by":"publisher","first-page":"2669","DOI":"10.1023\/A:1026680806775","volume":"37","author":"CJ Isham","year":"1998","unstructured":"Isham, C.J., Butterfield, J.: A Topos perspective on the Kochen-Specker theorem I. Quantum states as generalized valuations, Internat. J. Theoret. Phys. 37, 2669\u20132733 (1998)","journal-title":"J. Theoret. Phys."},{"key":"9531_CR26","doi-asserted-by":"publisher","first-page":"827","DOI":"10.1023\/A:1026652817988","volume":"38","author":"CJ Isham","year":"1999","unstructured":"Isham, C.J., Butterfield, J.: A Topos perspective on the Kochen-Specker theorem. II. Conceptual aspects, and quantum analogs, Internat. J. Theoret. Phys. 38, 827\u2013859 (1999)","journal-title":"J. Theoret. Phys."},{"key":"9531_CR27","doi-asserted-by":"publisher","first-page":"1413","DOI":"10.1023\/A:1003667607842","volume":"39","author":"CJ Isham","year":"2000","unstructured":"Isham, C.J., Hamilton, J., Butterfield, J.: A Topos perspective on the Kochen-Specker theorem. III. Von Neumann algebras as the base category, Internat. J. Theoret. Phys. 39, 1413\u20131436 (2000)","journal-title":"J. Theoret. Phys."},{"key":"9531_CR28","doi-asserted-by":"publisher","first-page":"613","DOI":"10.1023\/A:1015276209768","volume":"41","author":"CJ Isham","year":"2002","unstructured":"Isham, C.J., Butterfield, J.: A Topos perspective on the Kochen-Specker theorem. IV. Interval valuations, Internat. J. Theoret. Phys. 41, 613\u2013639 (2002)","journal-title":"J. Theoret. Phys."},{"key":"9531_CR29","volume-title":"Fundamentals of the Theory of Operator Algebras. Vol. I: Elementary Theory","author":"RV Kadison","year":"1983","unstructured":"Kadison, R.V., Ringrose, J.R.: Fundamentals of the Theory of Operator Algebras. Vol. I: Elementary Theory. Academic Press, New York (1983)"},{"key":"9531_CR30","unstructured":"Kochen, S., Specker, E.P. In: Addison, J.W., Henkin, L., Tarski, A. (eds.) : Logical Structures Arising in Quantum Theory, The Theory of Models. Amsterdam, North-Holland (1965)"},{"key":"9531_CR31","doi-asserted-by":"publisher","first-page":"174","DOI":"10.4204\/EPTCS.236.12","volume":"236","author":"F Roumen","year":"2017","unstructured":"Roumen, F.: Cohomology of effect algebras, Proceedings QPL. EPTCS 236, 174\u2013201 (2017)","journal-title":"EPTCS"},{"key":"9531_CR32","unstructured":"Wolters, S.: A comparison of two topos-theoretic approaches to quantum theory. arXiv:1010.2031 (2011)"}],"container-title":["Order"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11083-020-09531-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11083-020-09531-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11083-020-09531-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,10,29]],"date-time":"2022-10-29T11:12:27Z","timestamp":1667041947000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11083-020-09531-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,6,19]]},"references-count":32,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2021,4]]}},"alternative-id":["9531"],"URL":"https:\/\/doi.org\/10.1007\/s11083-020-09531-6","relation":{},"ISSN":["0167-8094","1572-9273"],"issn-type":[{"value":"0167-8094","type":"print"},{"value":"1572-9273","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,6,19]]},"assertion":[{"value":"30 September 2019","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"22 May 2020","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"19 June 2020","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}