{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,3,24]],"date-time":"2024-03-24T19:10:39Z","timestamp":1711307439531},"reference-count":30,"publisher":"Springer Science and Business Media LLC","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Order"],"published-print":{"date-parts":[[2010,7]]},"DOI":"10.1007\/s11083-010-9147-3","type":"journal-article","created":{"date-parts":[[2010,3,9]],"date-time":"2010-03-09T06:55:17Z","timestamp":1268117717000},"page":"225-233","source":"Crossref","is-referenced-by-count":0,"title":["Constructive Pointfree Topology Eliminates Non-constructive Representation Theorems from Riesz Space Theory"],"prefix":"10.1007","volume":"27","author":[{"given":"Bas","family":"Spitters","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2010,3,10]]},"reference":[{"issue":"4","key":"9147_CR1","doi-asserted-by":"crossref","first-page":"423","DOI":"10.1016\/0019-3577(91)90028-6","volume":"2","author":"G Buskes","year":"1991","unstructured":"Buskes, G., de Pagter, B., van Rooij, A.: Functional calculus on Riesz spaces. Indag. Math. (N.S.) 2(4), 423\u2013436 (1991)","journal-title":"Indag. Math. (N.S.)"},{"issue":"2","key":"9147_CR2","doi-asserted-by":"crossref","first-page":"298","DOI":"10.2307\/1968871","volume":"43","author":"G Birkhoff","year":"1942","unstructured":"Birkhoff, G.: Lattice ordered groups. Ann. Math. 43(2), 298\u2013331 (1942)","journal-title":"Ann. Math."},{"issue":"1\u20133","key":"9147_CR3","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1016\/S0022-4049(96)00160-0","volume":"116","author":"B Banaschewski","year":"1997","unstructured":"Banaschewski, B., Mulvey, C.J.: A constructive proof of the Stone-Weierstrass theorem. J. Pure Appl. Algebra, 116(1\u20133), 25\u201340 (1997). Special volume on the occasion of the 60th birthday of Professor Peter J. Freyd","journal-title":"J. Pure Appl. Algebra"},{"issue":"4","key":"9147_CR4","doi-asserted-by":"crossref","first-page":"465","DOI":"10.2989\/16073600009485990","volume":"23","author":"B Banaschewski","year":"2000","unstructured":"Banaschewski, B., Mulvey, C.J.: The spectral theory of commutative C *-algebras: the constructive Gelfand-Mazur theorem. Quaest. Math. 23(4), 465\u2013488 (2000)","journal-title":"Quaest. Math."},{"issue":"4","key":"9147_CR5","doi-asserted-by":"crossref","first-page":"425","DOI":"10.2989\/16073600009485989","volume":"23","author":"B Banaschewski","year":"2000","unstructured":"Banaschewski, B., Mulvey, C.J.: The spectral theory of commutative C *-algebras: the constructive spectrum. Quaest. Math. 23(4), 425\u2013464 (2000)","journal-title":"Quaest. Math."},{"issue":"1\u20133","key":"9147_CR6","doi-asserted-by":"crossref","first-page":"62","DOI":"10.1016\/j.apal.2005.05.018","volume":"137","author":"B Banaschewski","year":"2006","unstructured":"Banaschewski, B., Mulvey, C.J.: A globalisation of the Gelfand duality theorem. Ann. Pure Appl. Logic 137(1\u20133), 62\u2013103 (2006)","journal-title":"Ann. Pure Appl. Logic"},{"issue":"3","key":"9147_CR7","doi-asserted-by":"crossref","first-page":"523","DOI":"10.1017\/S0305004100077902","volume":"105","author":"G Buskes","year":"1989","unstructured":"Buskes, G., van Rooij, A.: Small Riesz spaces. Math. Proc. Camb. Philos. Soc. 105(3), 523\u2013536 (1989)","journal-title":"Math. Proc. Camb. Philos. Soc."},{"issue":"3","key":"9147_CR8","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1023\/A:1009826510957","volume":"4","author":"G Buskes","year":"2000","unstructured":"Buskes, G., van Rooij, A.: Almost f-algebras: commutativity and the Cauchy-Schwarz inequality. Positivity 4(3), 227\u2013231 (2000). Positivity and its applications (Ankara, 1998)","journal-title":"Positivity"},{"key":"9147_CR9","series-title":"Lect. Notes Log","first-page":"127","volume-title":"Logic Colloquium \u201998 (Prague)","author":"J Cederquist","year":"2000","unstructured":"Cederquist, J., Coquand, T.: Entailment relations and distributive lattices. In: Logic Colloquium \u201998 (Prague). Lect. Notes Log., vol. 13, pp. 127\u2013139. Assoc. Symbol. Logic, Urbana, IL (2000)"},{"issue":"7","key":"9147_CR10","doi-asserted-by":"crossref","first-page":"731","DOI":"10.1007\/s10701-009-9308-7","volume":"39","author":"M Caspers","year":"2009","unstructured":"Caspers, M., Heunen, C., Landsman, K., Spitters, B.: Intuitionistic quantum logic of an n-level system. Found. Phys. 39(7), 731\u2013759 (2009)","journal-title":"Found. Phys."},{"issue":"1","key":"9147_CR11","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/S0022-4049(03)00088-4","volume":"184","author":"T Coquand","year":"2003","unstructured":"Coquand, T.: Compact spaces and distributive lattices. J. Pure Appl. Algebra 184(1), 1\u20136 (2003)","journal-title":"J. Pure Appl. Algebra"},{"key":"9147_CR12","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1016\/j.jpaa.2004.08.024","volume":"197","author":"T Coquand","year":"2005","unstructured":"Coquand, T.: About Stone\u2019s notion of spectrum. J. Pure Appl. Algebra 197, 141\u2013158 (2005)","journal-title":"J. Pure Appl. Algebra"},{"issue":"12","key":"9147_CR13","first-page":"1932","volume":"11","author":"T Coquand","year":"2005","unstructured":"Coquand, T., Spitters, B.: Formal topology and constructive mathematics: the Gelfand and Stone-Yosida representation theorems. J. Univers. Comput. Sci. 11(12), 1932\u20131944 (2005)","journal-title":"J. Univers. Comput. Sci."},{"issue":"2","key":"9147_CR14","doi-asserted-by":"crossref","first-page":"323","DOI":"10.1017\/S0305004109002539","volume":"147","author":"B Spitters","year":"2009","unstructured":"Coquand, T., Spitters, B.: A constructive proof of Gelfand duality for C*-algebras. Math. Proc. Camb. Philos. Soc. 147(2), 323\u2013337 (2009). doi: 10.1017\/S0305004109002539","journal-title":"Math. Proc. Camb. Philos. Soc."},{"key":"9147_CR15","volume-title":"Partially Ordered Algebraic Systems","author":"L Fuchs","year":"1963","unstructured":"Fuchs, L.: Partially Ordered Algebraic Systems. Pergamon Press, Oxford (1963)"},{"issue":"1","key":"9147_CR16","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1007\/s00220-009-0865-6","volume":"291","author":"C Heunen","year":"2009","unstructured":"Heunen, C., Landsman, K., Spitters, B.: A topos for algebraic quantum theory. Commun. Math. Phys. 291(1), 63\u2013110 (2009)","journal-title":"Commun. Math. Phys."},{"key":"9147_CR17","unstructured":"Heunen, C., Landsman, N.P., Spitters, B.: Bohrification of Operator Algebras and Quantum Logic (2009)"},{"key":"9147_CR18","doi-asserted-by":"crossref","unstructured":"Johnstone, P.T.: Sketches of an Elephant: a Topos Theory Compendium, vol.\u00a02. Clarendon Press (2002)","DOI":"10.1093\/oso\/9780198515982.001.0001"},{"key":"9147_CR19","doi-asserted-by":"crossref","first-page":"533","DOI":"10.1007\/BF01580299","volume":"45","author":"P Lorenzen","year":"1939","unstructured":"Lorenzen, P.: Abstrakte Begr\u00fcndung der multiplikativen Idealtheorie. Math. Z. 45, 533\u2013553 (1939)","journal-title":"Math. Z."},{"key":"9147_CR20","volume-title":"Riesz Spaces, vol. I. North-Holland Mathematical Library","author":"WAJ Luxemburg","year":"1971","unstructured":"Luxemburg, W.A.J., Zaanen, A.C.: Riesz Spaces, vol. I. North-Holland Mathematical Library. North-Holland Publishing Co., Amsterdam (1971)"},{"key":"9147_CR21","doi-asserted-by":"crossref","unstructured":"Mac Lane, S., Moerdijk, I.: Sheaves in Geometry and Logic. Universitext. Springer-Verlag, New York (1994) A first introduction to topos theory. Corrected reprint of the 1992 edition","DOI":"10.1007\/978-1-4612-0927-0"},{"key":"9147_CR22","series-title":"Trends Log. Stud. Log. Libr","doi-asserted-by":"crossref","first-page":"309","DOI":"10.1007\/978-94-017-0231-7_13","volume-title":"Topological and Algebraic Structures in Fuzzy Sets","author":"CJ Mulvey","year":"2003","unstructured":"Mulvey, C.J.: On the geometry of choice. In: Topological and Algebraic Structures in Fuzzy Sets. Trends Log. Stud. Log. Libr., vol. 20, pp. 309\u2013336. Kluwer Acad. Publ., Dordrecht (2003)"},{"issue":"2","key":"9147_CR23","doi-asserted-by":"crossref","first-page":"174","DOI":"10.2307\/1968825","volume":"41","author":"F Riesz","year":"1940","unstructured":"Riesz, F.: Sur quelques notions fondamentales dans la th\u00e9orie g\u00e9n\u00e9rale des op\u00e9rations lin\u00e9aires. Ann. Math. 41(2), 174\u2013206 (1940)","journal-title":"Ann. Math."},{"key":"9147_CR24","doi-asserted-by":"crossref","unstructured":"Sambin, G.: Intuitionistic formal spaces - a first communication. In: Skordev, D. (ed.) Mathematical Logic and Its Applications, pp. 187\u2013204. Plenum (1987)","DOI":"10.1007\/978-1-4613-0897-3_12"},{"key":"9147_CR25","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1073\/pnas.27.1.83","volume":"27","author":"MH Stone","year":"1941","unstructured":"Stone, M.H.: A general theory of spectra. II. Proc. Nat. Acad. Sci. U. S. A. 27, 83\u201387 (1941)","journal-title":"Proc. Nat. Acad. Sci. U. S. A."},{"key":"9147_CR26","volume-title":"Kan\u00f4 Memorial Lectures, vol. 3. Publications of the Mathematical Society of Japan, No. 13","author":"G Takeuti","year":"1978","unstructured":"Takeuti, G.: Two applications of logic to mathematics. In: Kan\u00f4 Memorial Lectures, vol. 3. Publications of the Mathematical Society of Japan, No. 13. Iwanami Shoten, Publishers, Tokyo (1978)"},{"key":"9147_CR27","doi-asserted-by":"crossref","unstructured":"Vickers, S.: Locales and toposes as spaces. In: Aiello, M., Pratt-Hartmann, I.E., van Benthem, J.F.A.K. (eds.) Handbook of Spatial Logics, chapter\u00a08. Springer (2007)","DOI":"10.1007\/978-1-4020-5587-4_8"},{"key":"9147_CR28","doi-asserted-by":"crossref","first-page":"339","DOI":"10.3792\/pia\/1195573861","volume":"18","author":"K Yosida","year":"1942","unstructured":"Yosida, K.: On the representation of the vector lattice. Proc. Imp. Acad. Tokyo 18, 339\u2013342 (1942)","journal-title":"Proc. Imp. Acad. Tokyo"},{"key":"9147_CR29","volume-title":"North-Holland Mathematical Library, vol. 30","author":"AC Zaanen","year":"1983","unstructured":"Zaanen, A.C.: Riesz spaces. II. In: North-Holland Mathematical Library, vol. 30. North-Holland Publishing Co., Amsterdam (1983)"},{"key":"9147_CR30","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-60637-3","volume-title":"Introduction to Operator Theory in Riesz Spaces","author":"AC Zaanen","year":"1997","unstructured":"Zaanen, A.C.: Introduction to Operator Theory in Riesz Spaces. Springer-Verlag, Berlin (1997)"}],"container-title":["Order"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.springerlink.com\/index\/pdf\/10.1007\/s11083-010-9147-3","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,3,24]],"date-time":"2024-03-24T18:40:37Z","timestamp":1711305637000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11083-010-9147-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,3,10]]},"references-count":30,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2010,7]]}},"alternative-id":["9147"],"URL":"https:\/\/doi.org\/10.1007\/s11083-010-9147-3","relation":{},"ISSN":["0167-8094","1572-9273"],"issn-type":[{"value":"0167-8094","type":"print"},{"value":"1572-9273","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,3,10]]}}}