{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,31]],"date-time":"2022-03-31T23:11:42Z","timestamp":1648768302325},"reference-count":12,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":6036,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1997,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Gurevich and Shelah have shown that Peano Arithmetic cannot be interpreted in the monadic second-order theory of short chains (hence, in the monadic second-order theory of the real line). We will show here that it is consistent that the monadic second-order theory of no chain interprets Peano Arithmetic.<\/jats:p>","DOI":"10.2307\/2275575","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T19:01:58Z","timestamp":1146942118000},"page":"848-872","source":"Crossref","is-referenced-by-count":1,"title":["Peano arithmetic may not be interpretable in the monadic theory of linear orders"],"prefix":"10.1017","volume":"62","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":"S0022481200016054_ref012","first-page":"98","volume-title":"Undecidable theories","author":"Tarski","year":"1953"},{"key":"S0022481200016054_ref008","doi-asserted-by":"publisher","DOI":"10.1007\/BF02760646"},{"key":"S0022481200016054_ref010","doi-asserted-by":"publisher","DOI":"10.2307\/1971037"},{"key":"S0022481200016054_ref003","first-page":"479","volume-title":"Monadic second-order theories","author":"Gurevich","year":"1985"},{"key":"S0022481200016054_ref011","doi-asserted-by":"publisher","DOI":"10.1007\/BF02764732"},{"key":"S0022481200016054_ref004","first-page":"387","volume":"48","author":"Gurevich","year":"1983","journal-title":"The monadic theory of \u03c92"},{"key":"S0022481200016054_ref009","unstructured":"Lifsches S. and Shelah S. , Random graphs in the monadic theory of order, in preparation."},{"key":"S0022481200016054_ref001","first-page":"445","volume-title":"Model theoretic logics","author":"Baldwin","year":"1985"},{"key":"S0022481200016054_ref002","doi-asserted-by":"publisher","DOI":"10.1305\/ndjfl\/1093870870"},{"key":"S0022481200016054_ref005","first-page":"305","volume":"54","author":"Gurevich","year":"1989","journal-title":"On the strength of the interpretation method"},{"key":"S0022481200016054_ref006","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4843(82)90004-3"},{"key":"S0022481200016054_ref007","first-page":"816","volume":"48","author":"Gurevich","year":"1983","journal-title":"Interpreting second-order logic in the monadic theory of order"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200016054","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,11]],"date-time":"2019-05-11T16:25:02Z","timestamp":1557591902000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200016054\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1997,9]]},"references-count":12,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1997,9]]}},"alternative-id":["S0022481200016054"],"URL":"https:\/\/doi.org\/10.2307\/2275575","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1997,9]]}}}