{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,5]],"date-time":"2024-09-05T01:36:47Z","timestamp":1725500207189},"publisher-location":"Berlin, Heidelberg","reference-count":33,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783540776635"},{"type":"electronic","value":"9783540776642"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"DOI":"10.1007\/978-3-540-77664-2_18","type":"book-chapter","created":{"date-parts":[[2008,1,10]],"date-time":"2008-01-10T10:18:25Z","timestamp":1199960305000},"page":"231-244","source":"Crossref","is-referenced-by-count":7,"title":["Completions of Ordered Algebraic Structures: A Survey"],"prefix":"10.1007","author":[{"given":"John","family":"Harding","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"18_CR1","doi-asserted-by":"publisher","first-page":"250","DOI":"10.1007\/BF02485732","volume":"4","author":"K.A. Baker","year":"1974","unstructured":"Baker, K.A., Hales, A.W.: From a lattice to its ideal lattice. Algebra Universalis\u00a04, 250\u2013258 (1974)","journal-title":"Algebra Universalis"},{"key":"18_CR2","first-page":"35","volume":"2","author":"B. Banaschewski","year":"1956","unstructured":"Banaschewski, B.: H\u00fcllensysteme und Erweiterungen von Quasi-Ordnungen. Z. Math. Logik Grund. Math.\u00a02, 35\u201346 (1956)","journal-title":"Z. Math. Logik Grund. Math."},{"key":"18_CR3","doi-asserted-by":"crossref","first-page":"369","DOI":"10.1007\/BF01898828","volume":"18","author":"B. Banaschewski","year":"1967","unstructured":"Banaschewski, B., Bruns, G.: Categorical characterization of the MacNeille completion. Arch. Math (Basel)\u00a018, 369\u2013377 (1967)","journal-title":"Arch. Math. (Basel)"},{"issue":"2","key":"18_CR4","doi-asserted-by":"publisher","first-page":"209","DOI":"10.1023\/B:STUD.0000037127.15182.2a","volume":"77","author":"F. Belardinelli","year":"2004","unstructured":"Belardinelli, F., Jipsen, P., Ono, H.: Algebraic aspects of cut elimination. Studia Logica\u00a077(2), 209\u2013240 (2004)","journal-title":"Studia Logica"},{"issue":"4","key":"18_CR5","first-page":"937","volume":"30","author":"G. Bezhanishvili","year":"2004","unstructured":"Bezhanishvili, G., Harding, J.: MacNeille completions of Heyting algebras. The Houston J. of Math.\u00a030(4), 937\u2013952 (2004)","journal-title":"The Houston J. of Math."},{"issue":"2","key":"18_CR6","first-page":"355","volume":"33","author":"G. Bezhanishvili","year":"2007","unstructured":"Bezhanishvili, G., Harding, J.: MacNeille completions of modal algebras. The Houston J. of Math.\u00a033(2), 355\u2013384 (2007)","journal-title":"The Houston J. of Math."},{"key":"18_CR7","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9781107050884","volume-title":"Modal Logic","author":"P. Blackburn","year":"2001","unstructured":"Blackburn, P., de Rijke, M., Venema, Y.: Modal Logic. Cambridge University Press, Cambridge (2001)"},{"key":"18_CR8","unstructured":"Birkhoff, G.: Lattice Theory. In: Amer. Math. Soc. Coll. Publ., 3rd edn., vol. 25, Amer. Math. Soc., Providence (1967)"},{"key":"18_CR9","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4613-8130-3","volume-title":"A Course in Universal Algebra","author":"S. Burris","year":"1981","unstructured":"Burris, S., Sankappanavar, H.P.: A Course in Universal Algebra. Springer, Heidelberg (1981)"},{"key":"18_CR10","volume-title":"Algebraic Theory of Lattices","author":"P. Crawley","year":"1973","unstructured":"Crawley, P., Dilworth, R.P.: Algebraic Theory of Lattices. Prentice-Hall, New Jersey (1973)"},{"issue":"2","key":"18_CR11","doi-asserted-by":"publisher","first-page":"175","DOI":"10.1007\/BF00389840","volume":"13","author":"G.D. Crown","year":"1996","unstructured":"Crown, G.D., Harding, J., Janowitz, M.F.: Boolean products of lattices. Order\u00a013(2), 175\u2013205 (1996)","journal-title":"Order"},{"key":"18_CR12","volume-title":"Essays on the Theory of Numbers","author":"R. Dedekind","year":"1963","unstructured":"Dedekind, R.: Essays on the Theory of Numbers. Dover, New York (1963)"},{"issue":"2","key":"18_CR13","doi-asserted-by":"publisher","first-page":"241","DOI":"10.1007\/s11225-006-9008-7","volume":"84","author":"M. Gehrke","year":"2006","unstructured":"Gehrke, M.: Generalized Kripke frames. Studia Logica\u00a084(2), 241\u2013275 (2006)","journal-title":"Studia Logica"},{"key":"18_CR14","doi-asserted-by":"publisher","first-page":"345","DOI":"10.1006\/jabr.2000.8622","volume":"238","author":"M. Gehrke","year":"2001","unstructured":"Gehrke, M., Harding, J.: Bounded lattice expansions. J. Algebra\u00a0238, 345\u2013371 (2001)","journal-title":"J. Algebra"},{"issue":"2","key":"18_CR15","doi-asserted-by":"publisher","first-page":"573","DOI":"10.1090\/S0002-9947-05-03816-X","volume":"358","author":"M. Gehrke","year":"2005","unstructured":"Gehrke, M., Harding, J., Venema, Y.: MacNeille completions and canonical extensions. Trans. Amer. Math. Soc.\u00a0358(2), 573\u2013590 (2005)","journal-title":"Trans. Amer. Math. Soc."},{"key":"18_CR16","doi-asserted-by":"crossref","first-page":"13","DOI":"10.7146\/math.scand.a-14428","volume":"94","author":"M. Gehrke","year":"2004","unstructured":"Gehrke, M., J\u00f3nsson, B.: Bounded distributive lattice expansions. Math. Scand.\u00a094, 13\u201345 (2004)","journal-title":"Math. Scand."},{"issue":"1\u20133","key":"18_CR17","doi-asserted-by":"publisher","first-page":"65","DOI":"10.1016\/j.apal.2004.04.007","volume":"131","author":"M. Gehrke","year":"2005","unstructured":"Gehrke, M., Nagahashi, H., Venema, Y.: A Sahlqvist theorem for distributive modal logic. Ann. Pure Applied Logic\u00a0131(1\u20133), 65\u2013102 (2005)","journal-title":"Ann. Pure Applied Logic"},{"key":"18_CR18","doi-asserted-by":"publisher","first-page":"47","DOI":"10.1007\/s000120050100","volume":"41","author":"S. Givant","year":"1999","unstructured":"Givant, S., Venema, Y.: The preservation of Sahlqvist equations in completions of Boolean algebras with operators. Algebra Universalis\u00a041, 47\u201384 (1999)","journal-title":"Algebra Universalis"},{"key":"18_CR19","doi-asserted-by":"publisher","first-page":"186","DOI":"10.2178\/bsl\/1082986262","volume":"10","author":"R. Goldblatt","year":"2004","unstructured":"Goldblatt, R., Hodkinson, I., Venema, Y.: Erd\u00f6s graphs resolve Fine\u2019s canonicity problem. Bull. of Symbolic Logic\u00a010, 186\u2013208 (2004)","journal-title":"Bull. of Symbolic Logic"},{"key":"18_CR20","first-page":"39","volume":"19","author":"J. Harding","year":"1993","unstructured":"Harding, J.: Any lattice can be regularly embedded into the MacNeille completion of a distributive lattice. The Houston J. of Math.\u00a019, 39\u201344 (1993)","journal-title":"The Houston J. of Math."},{"key":"18_CR21","first-page":"85","volume":"15","author":"J. Harding","year":"1998","unstructured":"Harding, J.: Canonical completions of lattices and ortholattices. Tatra Mountains Math. Publ.\u00a015, 85\u201396 (1998)","journal-title":"Tatra Mountains Math. Publ."},{"key":"18_CR22","unstructured":"Harding, J.: A regular completion for the variety generated by the three-element Heyting algebra. The Houston J. of Math (to appear)"},{"key":"18_CR23","unstructured":"Harding, J.: Unpublished manuscript"},{"key":"18_CR24","doi-asserted-by":"publisher","first-page":"891","DOI":"10.2307\/2372123","volume":"73","author":"B. J\u00f3nsson","year":"1951","unstructured":"J\u00f3nsson, B., Tarski, A.: Boolean algebras with operators I. Amer. J. of Math.\u00a073, 891\u2013939 (1951)","journal-title":"Amer. J. of Math."},{"key":"18_CR25","doi-asserted-by":"publisher","first-page":"127","DOI":"10.2307\/2372074","volume":"74","author":"B. J\u00f3nsson","year":"1952","unstructured":"J\u00f3nsson, B., Tarski, A.: Boolean algebras with operators II. Amer. J. of Math.\u00a074, 127\u2013162 (1952)","journal-title":"Amer. J. of Math."},{"issue":"4","key":"18_CR26","doi-asserted-by":"publisher","first-page":"473","DOI":"10.1007\/BF01057646","volume":"53","author":"B. J\u00f3nsson","year":"1994","unstructured":"J\u00f3nsson, B.: On the canonicity of Sahlqvist identities. Studia Logica\u00a053(4), 473\u2013491 (1994)","journal-title":"Studia Logica"},{"key":"18_CR27","doi-asserted-by":"crossref","unstructured":"Kowalski, T., Litak, T.: Completions of GBL algebras: Negative results. Algebra Universalis (to appear)","DOI":"10.1007\/s00012-008-2056-2"},{"key":"18_CR28","doi-asserted-by":"publisher","first-page":"416","DOI":"10.2307\/1989739","volume":"42","author":"H.M. MacNeille","year":"1937","unstructured":"MacNeille, H.M.: Partially ordered sets. Trans. Amer. Math. Soc.\u00a042, 416\u2013460 (1937)","journal-title":"Trans. Amer. Math. Soc."},{"key":"18_CR29","doi-asserted-by":"publisher","first-page":"47","DOI":"10.1002\/mana.19700460105","volume":"46","author":"J.D. Monk","year":"1970","unstructured":"Monk, J.D.: Completions of Boolean algebras with operators. Mathematische Nachrichten\u00a046, 47\u201355 (1970)","journal-title":"Mathematische Nachrichten"},{"key":"18_CR30","doi-asserted-by":"crossref","unstructured":"Sahlqvist, H.: Completeness and correspondence in the first and second order semantics for modal logic. In: Proceedings of the Third Scandinavian Logic Symposium, Univ. Uppsala, Uppsala, pp. 110\u2013143 (1973), Stud. Logic Found. Math. 82, North-Holland, Amsterdam (1975)","DOI":"10.1016\/S0049-237X(08)70728-6"},{"key":"18_CR31","doi-asserted-by":"publisher","first-page":"241","DOI":"10.1007\/BF01900297","volume":"7","author":"J. Schmidt","year":"1956","unstructured":"Schmidt, J.: Zur Kennzeichnung der Dedekind-MacNeilleschen H\u00fclle einer geordneten Menge. Archiv. d. Math.\u00a07, 241\u2013249 (1956)","journal-title":"Archiv. d. Math."},{"key":"18_CR32","doi-asserted-by":"publisher","first-page":"45","DOI":"10.1007\/BF02485369","volume":"8","author":"A. Urquhart","year":"1978","unstructured":"Urquhart, A.: A topological representation theory for lattices. Algebra Universalis\u00a08, 45\u201358 (1978)","journal-title":"Algebra Universalis"},{"key":"18_CR33","unstructured":"Venema, Y.: Personal communication"}],"container-title":["Advances in Soft Computing","Interval \/ Probabilistic Uncertainty and Non-Classical Logics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-540-77664-2_18.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,4,27]],"date-time":"2021-04-27T10:47:51Z","timestamp":1619520471000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-540-77664-2_18"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[null]]},"ISBN":["9783540776635","9783540776642"],"references-count":33,"URL":"https:\/\/doi.org\/10.1007\/978-3-540-77664-2_18","relation":{},"subject":[]}}