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The following results are established: In 0<jats:sup>\u00b6<\/jats:sup>the hom sets are precisely the<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200001146_inline01\" \/>sets. In<jats:italic>M<jats:sub>n<\/jats:sub><\/jats:italic>every hom set is correctly<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200001146_inline02\" \/>, and (<jats:italic>\u03b4<\/jats:italic>+ 1)-universally Baire where<jats:italic>\u03b4<\/jats:italic>is the least Woodin. In<jats:italic>M<\/jats:italic><jats:sub><jats:italic>\u03c9<\/jats:italic><\/jats:sub>, every hom set is &lt;<jats:italic>\u03bb<\/jats:italic>-hom, where<jats:italic>\u03bb<\/jats:italic>is the supremum of the Woodins.<\/jats:p>","DOI":"10.2178\/jsl.7704040","type":"journal-article","created":{"date-parts":[[2012,11,2]],"date-time":"2012-11-02T19:23:52Z","timestamp":1351884232000},"page":"1122-1146","source":"Crossref","is-referenced-by-count":2,"title":["Homogeneously Suslin sets in tame mice"],"prefix":"10.1017","volume":"77","author":[{"given":"Farmer","family":"Schlutzenberg","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200001146_ref011","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4020-5764-9_23"},{"key":"S0022481200001146_ref021","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4020-5764-9_20"},{"key":"S0022481200001146_ref002","first-page":"1601","volume":"64","author":"Hauser","year":"1999","journal-title":"A minimal counterexample to universalbaireness"},{"key":"S0022481200001146_ref019","doi-asserted-by":"crossref","unstructured":"Steel John R. , Derived models associated to mice, to appear; available from author's website, 2007.","DOI":"10.1142\/9789812794055_0003"},{"key":"S0022481200001146_ref018","unstructured":"Steel John R. , A stationary-tower-free proof of the derived model theorem, available from author's website, 2005."},{"key":"S0022481200001146_ref013","first-page":"241","volume":"71","author":"Schindler","year":"2006","journal-title":"Iterates of the core model"},{"key":"S0022481200001146_ref015","unstructured":"Schlutzenberg Farmer , Resurrection and iterability of fine extender models, unpublished notes, 2012."},{"key":"S0022481200001146_ref007","doi-asserted-by":"publisher","DOI":"10.1090\/S0894-0347-1994-1224594-7"},{"key":"S0022481200001146_ref001","first-page":"475","volume":"77","author":"Claverie","year":"2012","journal-title":"Woodin's axiom (*), bounded forcing axioms, and precipitous ideals on \u03c91"},{"key":"S0022481200001146_ref010","volume-title":"Descriptive set theory","author":"Moschovakis","year":"1980"},{"key":"S0022481200001146_ref017","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-22485-4"},{"key":"S0022481200001146_ref016","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(94)00021-T"},{"key":"S0022481200001146_ref008","doi-asserted-by":"publisher","DOI":"10.1090\/S0894-0347-1989-0955605-X"},{"key":"S0022481200001146_ref009","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-21903-4"},{"key":"S0022481200001146_ref006","volume-title":"The stationary tower: notes on a course by W. 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