{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,15]],"date-time":"2026-06-15T22:32:28Z","timestamp":1781562748741,"version":"3.54.5"},"reference-count":10,"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":5671,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1998,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>This paper concerns the theory of morasses. In the early 1970s Jensen defined (k, \u03b1)-morasses for uncountable regular cardinals <jats:italic>k<\/jats:italic> and ordinals \u03b1 &lt; <jats:italic>k<\/jats:italic>. In the early 1980s Velleman defined (<jats:italic>k<\/jats:italic>, 1)-simplified morasses for all regular cardinals <jats:italic>k<\/jats:italic>. He showed that there is a (<jats:italic>k<\/jats:italic>, 1)-simplified morass if and only if there is (<jats:italic>k<\/jats:italic>, 1)-morass. More recently he defined (<jats:italic>k<\/jats:italic>, 2)-simplified morasses and Jensen was able to show that if there is a (<jats:italic>k<\/jats:italic>, 2)-morass then there is a (<jats:italic>k<\/jats:italic>, 2)-simplified morass.<\/jats:p><jats:p>In this paper we prove the converse of Jensen's result, i.e., that if there is a (<jats:italic>k<\/jats:italic>, 2)-simplified morass then there is a (<jats:italic>k<\/jats:italic>, 2)-morass.<\/jats:p>","DOI":"10.2307\/2586711","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T14:01:28Z","timestamp":1146924088000},"page":"753-787","source":"Crossref","is-referenced-by-count":1,"title":["Higher gap morasses, Ia: Gap-two morasses and condensation"],"prefix":"10.1017","volume":"63","author":[{"given":"Charles","family":"Morgan","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200014584_ref008","doi-asserted-by":"crossref","unstructured":"Stanley L. , A short course on gap-one morasses and a review of the fine structure of L in \u201cSurveys in set theory\u201d, (A. R. D. Mathias, editor), London Mathematical Society Lecture Notes Series, vol. 87, 1982, pp. 197\u2013243.","DOI":"10.1017\/CBO9780511758867.008"},{"key":"S0022481200014584_ref010","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(87)90070-4"},{"key":"S0022481200014584_ref003","unstructured":"Dodd A. , Constructibility, two cardinals problems and the gap-n theorems, M. sc. dissertation , Oxford, 1974."},{"key":"S0022481200014584_ref009","first-page":"257","volume":"49","author":"Velleman","year":"1984","journal-title":"Simplified morasses"},{"key":"S0022481200014584_ref007","unstructured":"Devlin K. , Higher gap morasses, Ib: Finite gap morasses\u2014the general case, in preparation, 1993."},{"key":"S0022481200014584_ref004","doi-asserted-by":"publisher","DOI":"10.1090\/pspum\/042\/791060"},{"key":"S0022481200014584_ref006","unstructured":"Morgan C. J. G. , The equivalence of morasses and simplified morasses\u2014the general case, D. phil. thesis , Oxford, 1989."},{"key":"S0022481200014584_ref005","unstructured":"Jensen R. , There is a gap two Velleman morass in L, handwritten notes, circulated 1987."},{"key":"S0022481200014584_ref002","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-21723-8"},{"key":"S0022481200014584_ref001","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0059290"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200014584","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,10]],"date-time":"2019-05-10T16:21:06Z","timestamp":1557505266000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200014584\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1998,9]]},"references-count":10,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1998,9]]}},"alternative-id":["S0022481200014584"],"URL":"https:\/\/doi.org\/10.2307\/2586711","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1998,9]]}}}