{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,10]],"date-time":"2026-04-10T22:10:53Z","timestamp":1775859053063,"version":"3.50.1"},"reference-count":22,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":8685,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1990,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>A<jats:italic>topological classification scheme<\/jats:italic>consists of two ingredients: (1) an abstract class<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200025998_inline1\"\/>of topological spaces; and (2) a \u201ctaxonomy\u201d, i.e. a list of first order sentences, together with a way of assigning an abstract class of spaces to each sentence of the list so that logically equivalent sentences are assigned the same class.<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200025998_inline1\"\/>is then endowed with an equivalence relation, two spaces belonging to the same equivalence class if and only if they lie in the same classes prescribed by the taxonomy. A space<jats:italic>X<\/jats:italic>in<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200025998_inline1\"\/>is<jats:italic>characterized<\/jats:italic>within the classification scheme if whenever<jats:italic>Y<\/jats:italic>\u220a<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200025998_inline1\"\/>and<jats:italic>Y<\/jats:italic>is equivalent to<jats:italic>X<\/jats:italic>, then<jats:italic>Y<\/jats:italic>is homeomorphic to<jats:italic>X<\/jats:italic>. As prime example, the<jats:italic>closed set taxonomy<\/jats:italic>assigns to each sentence in the first order language of bounded lattices the class of topological spaces whose lattices of closed sets satisfy that sentence. It turns out that every compact two-complex is characterized via this taxonomy in the class of metrizable spaces, but that no infinite discrete space is so characterized. We investigate various natural classification schemes, compare them, and look into the question of which spaces can and cannot be characterized within them.<\/jats:p>","DOI":"10.2307\/2274649","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T22:35:29Z","timestamp":1146954929000},"page":"589-603","source":"Crossref","is-referenced-by-count":8,"title":["Taxonomies of model-theoretically defined topological properties"],"prefix":"10.1017","volume":"55","author":[{"given":"Paul","family":"Bankston","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200025998_ref015","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-9906-6"},{"key":"S0022481200025998_ref002","first-page":"478","volume":"49","author":"Bankston","year":"1984","journal-title":"Expressive power in first order topology"},{"key":"S0022481200025998_ref004","article-title":"Co-elementary equivalence for compact Hausdorff spaces and compact abelian groups","author":"Bankston","journal-title":"Journal of Pure and Applied Algebra"},{"key":"S0022481200025998_ref018","unstructured":"Swett A. K. , The first order topology of the real line (unpublished)."},{"key":"S0022481200025998_ref012","article-title":"First order topology","volume":"143","author":"Henson","year":"1977","journal-title":"Dissertationes Mathematicae\/Rozprawy Matematyczne"},{"key":"S0022481200025998_ref001","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1016\/S0016-660X(77)80006-8","article-title":"Ultraproducts in topology","volume":"7","author":"Bankston","year":"1977","journal-title":"General Topology and its Applications"},{"key":"S0022481200025998_ref003","first-page":"404","volume":"52","author":"Bankston","year":"1987","journal-title":"Reduced coproducts of compact Hausdorff spaces"},{"key":"S0022481200025998_ref006","volume-title":"Model theory","author":"Chang","year":"1973"},{"key":"S0022481200025998_ref008","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0097006"},{"key":"S0022481200025998_ref009","first-page":"294","volume":"53","author":"Gurevi\u010d","year":"1988","journal-title":"On ultracoproducts of compact Hausdorff spaces"},{"key":"S0022481200025998_ref010","first-page":"368","volume":"52","author":"Heinrich","year":"1987","journal-title":"A note on elementary equivalence of C(K) spaces"},{"key":"S0022481200025998_ref011","doi-asserted-by":"publisher","DOI":"10.1007\/BF02756565"},{"key":"S0022481200025998_ref022","first-page":"557","volume-title":"Model-theoretic logics","author":"Ziegler","year":"1985"},{"key":"S0022481200025998_ref014","volume-title":"Topology","volume":"2","author":"Kuratowski","year":"1968"},{"key":"S0022481200025998_ref016","volume-title":"Foundations of point set theory","author":"Moore","year":"1962"},{"key":"S0022481200025998_ref017","doi-asserted-by":"publisher","DOI":"10.2307\/1971037"},{"key":"S0022481200025998_ref020","doi-asserted-by":"publisher","DOI":"10.1090\/coll\/028"},{"key":"S0022481200025998_ref019","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-61935-9"},{"key":"S0022481200025998_ref021","volume-title":"General topology","author":"Willard","year":"1970"},{"key":"S0022481200025998_ref005","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1988-0937843-6"},{"key":"S0022481200025998_ref007","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0090160"},{"key":"S0022481200025998_ref013","volume-title":"Stone spaces","author":"Johnstone","year":"1982"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200025998","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,5,7]],"date-time":"2023-05-07T10:09:09Z","timestamp":1683454149000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200025998\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1990,6]]},"references-count":22,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1990,6]]}},"alternative-id":["S0022481200025998"],"URL":"https:\/\/doi.org\/10.2307\/2274649","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1990,6]]}}}