{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,6,12]],"date-time":"2022-06-12T21:19:27Z","timestamp":1655068767352},"reference-count":39,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":2568,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2007,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>A Turing degree <jats:bold>d<\/jats:bold> is <jats:italic>homogeneous bounding<\/jats:italic> if every complete decidable (CD) theory has a <jats:bold>d<\/jats:bold>-decidable homogeneous model <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200005612_inline1\" \/>, i.e., the elementary diagram <jats:italic>D<jats:sup>e<\/jats:sup><\/jats:italic> (<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200005612_inline1\" \/>) has degree <jats:bold>d<\/jats:bold>. It follows from results of Macintyre and Marker that every PA degree (i.e., every degree of a complete extension of Peano Arithmetic) is homogeneous bounding. We prove that in fact a degree is homogeneous bounding <jats:italic>if and only if<\/jats:italic> it is a PA degree. We do this by showing that there is a single CD theory <jats:italic>T<\/jats:italic> such that every homogeneous model of <jats:italic>T<\/jats:italic> has a <jats:bold>PA<\/jats:bold> degree.<\/jats:p>","DOI":"10.2178\/jsl\/1174668397","type":"journal-article","created":{"date-parts":[[2007,12,19]],"date-time":"2007-12-19T16:24:33Z","timestamp":1198081473000},"page":"305-323","source":"Crossref","is-referenced-by-count":2,"title":["Bounding homogenous models"],"prefix":"10.1017","volume":"72","author":[{"family":"Barbara F. 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