{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,14]],"date-time":"2026-03-14T00:09:00Z","timestamp":1773446940650,"version":"3.50.1"},"reference-count":47,"publisher":"Cambridge University Press (CUP)","issue":"8","license":[{"start":{"date-parts":[[2014,11,10]],"date-time":"2014-11-10T00:00:00Z","timestamp":1415577600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Struct. Comp. Sci."],"published-print":{"date-parts":[[2015,12]]},"abstract":"<jats:p>The structure of the Wadge degrees on zero-dimensional spaces is very simple (almost well ordered), but for many other natural nonzero-dimensional spaces (including the space of reals) this structure is much more complicated. We consider weaker notions of reducibility, including the so-called \u0394<jats:sup>0<\/jats:sup><jats:sub>\u03b1<\/jats:sub>-reductions, and try to find for various natural topological spaces <jats:italic>X<\/jats:italic> the least ordinal \u03b1<jats:sub><jats:italic>X<\/jats:italic><\/jats:sub> such that for every \u03b1<jats:sub><jats:italic>X<\/jats:italic><\/jats:sub> \u2a7d \u03b2 &lt; \u03c9<jats:sub>1<\/jats:sub> the degree-structure induced on <jats:italic>X<\/jats:italic> by the \u0394<jats:sup>0<\/jats:sup><jats:sub>\u03b2<\/jats:sub>-reductions is simple (i.e. similar to the Wadge hierarchy on the Baire space). We show that \u03b1<jats:sub><jats:italic>X<\/jats:italic><\/jats:sub> \u2a7d \u03c9 for every quasi-Polish space <jats:italic>X<\/jats:italic>, that \u03b1<jats:sub><jats:italic>X<\/jats:italic><\/jats:sub> \u2a7d 3 for quasi-Polish spaces of dimension \u2260 \u221e, and that this last bound is in fact optimal for many (quasi-)Polish spaces, including the real line and its powers.<\/jats:p>","DOI":"10.1017\/s0960129513000339","type":"journal-article","created":{"date-parts":[[2014,11,10]],"date-time":"2014-11-10T12:38:56Z","timestamp":1415623136000},"page":"1705-1754","source":"Crossref","is-referenced-by-count":13,"title":["Wadge-like reducibilities on arbitrary quasi-Polish spaces"],"prefix":"10.1017","volume":"25","author":[{"given":"LUCA","family":"MOTTO ROS","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"PHILIPP","family":"SCHLICHT","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"VICTOR","family":"SELIVANOV","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,11,10]]},"reference":[{"key":"S0960129513000339_ref20","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-03073-4_30"},{"key":"S0960129513000339_ref3","doi-asserted-by":"publisher","DOI":"10.4064\/fm177-2-5"},{"key":"S0960129513000339_ref45","doi-asserted-by":"publisher","DOI":"10.1090\/conm\/065\/891249"},{"key":"S0960129513000339_ref32","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2012.03.004"},{"key":"S0960129513000339_ref7","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2012.11.001"},{"key":"S0960129513000339_ref11","volume-title":"Princeton Mathematical Series","author":"Hurewicz","year":"1948"},{"key":"S0960129513000339_ref10","unstructured":"Hertling P. 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