{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,8,31]],"date-time":"2023-08-31T07:10:48Z","timestamp":1693465848190},"reference-count":22,"publisher":"Wiley","issue":"4-5","license":[{"start":{"date-parts":[[2004,8,18]],"date-time":"2004-08-18T00:00:00Z","timestamp":1092787200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[2004,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We present some characterizations of the members of \u0394<jats:sup>ta<\/jats:sup><jats:sub>2<\/jats:sub>, that class of the topological arithmetical hierarchy which is just large enough to include several fundamental types of sets of points in Euclidean spaces \u211d<jats:sup><jats:italic>k<\/jats:italic><\/jats:sup>. The limit characterization serves as a basic tool in further investigations. The characterization by effective difference chains of effectively exhaustible sets yields only a hierarchy within a subfield of \u0394<jats:sup>ta<\/jats:sup><jats:sub>2<\/jats:sub>. Effective difference chains of transfinite (but constructive) order types, consisting of complements of effectively exhaustible sets, as well as another closely related concept, yield a rich hierarchy within the whole class \u0394<jats:sup>ta<\/jats:sup><jats:sub>2<\/jats:sub>. The presentation always first reports analogies between Hausdorff's difference hierarchy within the Borel class \u0394<jats:sup>B<\/jats:sup><jats:sub>2<\/jats:sub> and Ershov's hierarchy within the class \u0394<jats:sup>0<\/jats:sup><jats:sub>2<\/jats:sub> of the arithmetical hierarchy; after that the counterparts for \u0394<jats:sup>ta<\/jats:sup><jats:sub>2<\/jats:sub> are developed. (\u00a9 2004 WILEY\u2010VCH Verlag GmbH &amp; Co. KGaA, Weinheim)<\/jats:p>","DOI":"10.1002\/malq.200310108","type":"journal-article","created":{"date-parts":[[2004,8,18]],"date-time":"2004-08-18T12:02:12Z","timestamp":1092830532000},"page":"507-519","source":"Crossref","is-referenced-by-count":5,"title":["Characterizations of the class \u0394<sup>ta<\/sup><sub>2<\/sub> over Euclidean spaces"],"prefix":"10.1002","volume":"50","author":[{"given":"Armin","family":"Hemmerling","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2004,8,18]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1002\/malq.19960420138"},{"key":"e_1_2_1_3_2","doi-asserted-by":"crossref","unstructured":"V.Brattka The emporer's new recursiveness: The epigraph of the exponential function in two models of computability. In: Words Languages and Combinatorics III (Masami Ito and Teruo Imaoka eds.) 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