{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,3]],"date-time":"2022-04-03T14:43:55Z","timestamp":1648997035044},"reference-count":7,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":6310,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1996,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The monadic second-order theory of trees allows quantification over elements and over arbitrary subsets. We classify the class of trees with respect to the question: does a tree <jats:italic>T<\/jats:italic> have a definable choice function (by a monadic formula with parameters)? A natural dichotomy arises where the trees that fall in the first class don't have a definable choice function and the trees in the second class have even a definable well ordering of their elements. This has a close connection to the uniformization problem.<\/jats:p>","DOI":"10.2307\/2275812","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T22:59:54Z","timestamp":1146956394000},"page":"1206-1227","source":"Crossref","is-referenced-by-count":6,"title":["Uniformization, choice functions and well orders in the class of trees"],"prefix":"10.1017","volume":"61","author":[{"given":"Shmuel","family":"Lifsches","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Saharon","family":"Shelah","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200016856_ref007","doi-asserted-by":"publisher","DOI":"10.2307\/1971037"},{"key":"S0022481200016856_ref006","first-page":"1","article-title":"Decidability of second-order theories and automata on infinite trees","volume":"141","author":"Rabin","year":"1969","journal-title":"Transactions of the American Mathematical Society"},{"key":"S0022481200016856_ref005","author":"Lifsches","journal-title":"Uniformization and Skolem functions in the class of trees"},{"key":"S0022481200016856_ref003","first-page":"1105","volume":"48","author":"Gurevich","year":"1983","journal-title":"Rabin's uniformization problem"},{"key":"S0022481200016856_ref001","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1969-0280205-0"},{"key":"S0022481200016856_ref002","first-page":"479","volume-title":"Model theoretic logics","author":"Gurevich","year":"1985"},{"key":"S0022481200016856_ref004","doi-asserted-by":"publisher","DOI":"10.1007\/BF01451165"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200016856","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,12]],"date-time":"2019-05-12T19:59:44Z","timestamp":1557691184000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200016856\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1996,12]]},"references-count":7,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1996,12]]}},"alternative-id":["S0022481200016856"],"URL":"https:\/\/doi.org\/10.2307\/2275812","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1996,12]]}}}