{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,9]],"date-time":"2026-10-09T07:36:04Z","timestamp":1791531364567,"version":"4.3.4"},"reference-count":25,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":923,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2011,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The first main result isolates some conditions which fail for the class of graphs and hold for the class of Abelian<jats:italic>p<\/jats:italic>-groups, the class of Abelian torsion groups, and the special class of \u201crank-homogeneous\u201d trees. We consider these conditions as a possible definition of what it means for a class of structures to have \u201cUlm type\u201d. The result says that there can be no Turing computable embedding of a class not of Ulm type into one of Ulm type. We apply this result to show that there is no Turing computable embedding of the class of graphs into the class of \u201crank-homogeneous\u201d trees. The second main result says that there is a Turing computable embedding of the class of rank-homogeneous trees into the class of torsion-free Abelian groups. The third main result says that there is a \u201crank-preserving\u201d Turing computable embedding of the class of rank-homogeneous trees into the class of Boolean algebras. Using this result, we show that there is a computable Boolean algebra of Scott rank<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200001559_inline3\"\/>.<\/jats:p>","DOI":"10.2178\/jsl\/1309952523","type":"journal-article","created":{"date-parts":[[2011,7,6]],"date-time":"2011-07-06T11:42:35Z","timestamp":1309952555000},"page":"846-869","source":"Crossref","is-referenced-by-count":13,"title":["Classes of Ulm type and coding rank-homogeneous trees in other structures"],"prefix":"10.1017","volume":"76","author":[{"given":"E.","family":"Fokina","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"J. F.","family":"Knight","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"A.","family":"Melnikov","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"S. M.","family":"Quinn","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"C.","family":"Safranski","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200001559_ref018","first-page":"301","volume":"46","author":"Makkai","year":"1981","journal-title":"An example concerning Scott heights"},{"key":"S0022481200001559_ref017","first-page":"901","volume":"73","author":"Knight","year":"2007","journal-title":"Turing computable embeddings"},{"key":"S0022481200001559_ref023","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4843(77)90009-2"},{"key":"S0022481200001559_ref004","first-page":"43","volume-title":"Advances in logic","author":"Calvert"},{"key":"S0022481200001559_ref002","first-page":"226","volume":"34","author":"Barwise","year":"1969","journal-title":"Infinitary logic and admissible sets"},{"key":"S0022481200001559_ref003","doi-asserted-by":"publisher","DOI":"10.1023\/B:ALLO.0000048827.30718.2c"},{"key":"S0022481200001559_ref011","unstructured":"Harizanov V. 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