{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,12]],"date-time":"2024-09-12T14:00:20Z","timestamp":1726149620475},"reference-count":18,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2018,8,1]],"date-time":"2018-08-01T00:00:00Z","timestamp":1533081600000},"content-version":"unspecified","delay-in-days":61,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2018,6]]},"abstract":"Abstract<\/jats:title>We show that from large cardinals it is consistent to have the tree property simultaneously at${\\aleph _{{\\omega ^2} + 1}}$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>and${\\aleph _{{\\omega ^2} + 2}}$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>with${\\aleph _{{\\omega ^2}}}$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>strong limit.<\/jats:p>","DOI":"10.1017\/jsl.2017.56","type":"journal-article","created":{"date-parts":[[2018,8,1]],"date-time":"2018-08-01T11:16:04Z","timestamp":1533122164000},"page":"669-682","source":"Crossref","is-referenced-by-count":5,"title":["THE TREE PROPERTY AT AND"],"prefix":"10.1017","volume":"83","author":[{"given":"DIMA","family":"SINAPOVA","sequence":"first","affiliation":[]},{"given":"SPENCER","family":"UNGER","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2018,8,1]]},"reference":[{"key":"S0022481217000561_ref5","unstructured":"[5] Friedman S.-D. , Honzik R. , and Stejskalov\u00e1 S. , The tree property at the double successor of a singular with a larger gap. Preprint, 2015. Available at logika.ff.cuni.cz\/sarka\/papers\/Friedman_Honzik_Stejskalova_A-tree-gap.pdf."},{"key":"S0022481217000561_ref18","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1016\/j.apal.2015.12.001","article-title":"The tree property below ${\\aleph _{\\omega \\cdot 2}}$.","volume":"167","author":"Specker","year":"2016","journal-title":"Annals of Pure and Applied Logic"},{"key":"S0022481217000561_ref9","doi-asserted-by":"publisher","DOI":"10.1007\/s001530050052"},{"key":"S0022481217000561_ref6","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-07-08716-3"},{"key":"S0022481217000561_ref4","doi-asserted-by":"publisher","DOI":"10.4064\/fm223-1-4"},{"key":"S0022481217000561_ref2","unstructured":"[2] Cox S. and Krueger J. , Quotients of strongly proper forcings and guessing models, this Journal, vol. 81 (2016), no. 1, pp. 264\u2013283."},{"key":"S0022481217000561_ref1","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(83)90006-4"},{"key":"S0022481217000561_ref17","doi-asserted-by":"crossref","first-page":"1110","DOI":"10.1016\/j.apal.2015.06.002","article-title":"Fragility and indestructibility II.","volume":"166","author":"Specker","year":"2015","journal-title":"Annals of Pure and Applied Logic"},{"key":"S0022481217000561_ref16","doi-asserted-by":"publisher","DOI":"10.1007\/s00153-013-0326-y"},{"key":"S0022481217000561_ref7","doi-asserted-by":"publisher","DOI":"10.4064\/fm-8-1-114-134"},{"key":"S0022481217000561_ref13","unstructured":"[13] Sinapova D. , The tree property and the failure of the singular cardinal hypothesis at ${\\aleph _{{\\omega ^2}}}$ , this Journal, vol. 77 (2012), no. 3, pp. 934\u2013946."},{"key":"S0022481217000561_ref11","doi-asserted-by":"publisher","DOI":"10.1142\/S021906130900080X"},{"key":"S0022481217000561_ref15","doi-asserted-by":"publisher","DOI":"10.4064\/cm-2-1-9-12"},{"key":"S0022481217000561_ref12","unstructured":"[12] Neeman I. , The tree property up to ${\\aleph _{\\omega + 1}}$ , this Journal, vol. 79 (2014), no. 2, pp. 429\u2013459."},{"key":"S0022481217000561_ref14","doi-asserted-by":"publisher","DOI":"10.1007\/s11856-016-1427-1"},{"key":"S0022481217000561_ref8","first-page":"1","article-title":"Ensembles ordonn\u00e9s et ramifi\u00e9s","volume":"vol. 4","author":"Kurepa","year":"1935","journal-title":"Publications de l\u2019Institut Math\u00e9matique,"},{"key":"S0022481217000561_ref3","doi-asserted-by":"publisher","DOI":"10.1006\/aima.1997.1680"},{"key":"S0022481217000561_ref10","doi-asserted-by":"crossref","unstructured":"[10] Mitchell W. , Aronszajn trees and the independence of the transfer property. Annals of Pure and Applied Logic, 5 (1972\/73), pp. 21\u201346.","DOI":"10.1016\/0003-4843(72)90017-4"}],"container-title":["The Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481217000561","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,10,21]],"date-time":"2019-10-21T17:04:14Z","timestamp":1571677454000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481217000561\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,6]]},"references-count":18,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2018,6]]}},"alternative-id":["S0022481217000561"],"URL":"https:\/\/doi.org\/10.1017\/jsl.2017.56","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,6]]}}}