{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,9,1]],"date-time":"2023-09-01T08:40:33Z","timestamp":1693557633307},"reference-count":4,"publisher":"Wiley","issue":"1-2","license":[{"start":{"date-parts":[[2012,1,4]],"date-time":"2012-01-04T00:00:00Z","timestamp":1325635200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[2012,2]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We analyze three applications of Ramsey\u2019s Theorem for 4\u2010tuples to infinite traceable graphs and finitely generated infinite lattices using the tools of reverse mathematics. The applications in graph theory are shown to be equivalent to Ramsey\u2019s Theorem while the application in lattice theory is shown to be provable in the weaker system RCA<jats:sub>0<\/jats:sub>.<\/jats:p>","DOI":"10.1002\/malq.201020066","type":"journal-article","created":{"date-parts":[[2012,1,5]],"date-time":"2012-01-05T02:19:55Z","timestamp":1325729995000},"page":"18-28","source":"Crossref","is-referenced-by-count":0,"title":["Reverse mathematics and infinite traceable graphs"],"prefix":"10.1002","volume":"58","author":[{"given":"Peter","family":"Cholak","sequence":"first","affiliation":[]},{"given":"David","family":"Galvin","sequence":"additional","affiliation":[]},{"given":"Reed","family":"Solomon","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2012,1,4]]},"reference":[{"key":"e_1_2_5_2_1","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(82)90053-3"},{"key":"e_1_2_5_3_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-22156-3"},{"key":"e_1_2_5_4_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-59971-2"},{"key":"e_1_2_5_5_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-02460-7"}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.201020066","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.201020066","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.201020066","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,8,31]],"date-time":"2023-08-31T16:53:51Z","timestamp":1693500831000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.201020066"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,1,4]]},"references-count":4,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2012,2]]}},"alternative-id":["10.1002\/malq.201020066"],"URL":"https:\/\/doi.org\/10.1002\/malq.201020066","archive":["Portico"],"relation":{},"ISSN":["0942-5616","1521-3870"],"issn-type":[{"value":"0942-5616","type":"print"},{"value":"1521-3870","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,1,4]]}}}