{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,1,9]],"date-time":"2023-01-09T23:28:23Z","timestamp":1673306903597},"reference-count":8,"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":5855,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1998,3]]},"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 definable Skolem functions (by a monadic formula with parameters)? This continues [6] where the question was asked only with respect to choice functions. A natural subclass is defined and proved to be the class of trees with definable Skolem functions. Along the way we investigate the spectrum of definable well orderings of well ordered chains.<\/jats:p>","DOI":"10.2307\/2586591","type":"journal-article","created":{"date-parts":[[2006,4,18]],"date-time":"2006-04-18T14:43:03Z","timestamp":1145371383000},"page":"103-127","source":"Crossref","is-referenced-by-count":13,"title":["Uniformization and skolem functions in the class of trees"],"prefix":"10.1017","volume":"63","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":"S002248120001536X_ref004","first-page":"1105","volume":"48","author":"Gurevich","year":"1983","journal-title":"Rabin's uniformization problem"},{"key":"S002248120001536X_ref008","doi-asserted-by":"publisher","DOI":"10.2307\/1971037"},{"key":"S002248120001536X_ref001","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1969-0280205-0"},{"key":"S002248120001536X_ref007","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":"S002248120001536X_ref006","first-page":"1206","volume":"61","author":"Lifsches","year":"1996","journal-title":"Uniformization, choice functions and well orders in the class of trees"},{"key":"S002248120001536X_ref002","doi-asserted-by":"publisher","DOI":"10.4064\/fm-47-1-57-103"},{"key":"S002248120001536X_ref003","first-page":"479","volume-title":"Model theoretic logics","author":"Gurevich","year":"1985"},{"key":"S002248120001536X_ref005","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\/S002248120001536X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,11]],"date-time":"2019-05-11T15:03:57Z","timestamp":1557587037000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S002248120001536X\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1998,3]]},"references-count":8,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1998,3]]}},"alternative-id":["S002248120001536X"],"URL":"https:\/\/doi.org\/10.2307\/2586591","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1998,3]]}}}