{"id":"https://openalex.org/W2137320411","doi":"https://doi.org/10.2307/2586711","title":"Higher gap morasses, Ia: Gap-two morasses and condensation","display_name":"Higher gap morasses, Ia: Gap-two morasses and condensation","publication_year":1998,"publication_date":"1998-09-01","ids":{"openalex":"https://openalex.org/W2137320411","doi":"https://doi.org/10.2307/2586711","mag":"2137320411"},"language":"en","primary_location":{"id":"doi:10.2307/2586711","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2586711","pdf_url":null,"source":{"id":"https://openalex.org/S177675236","display_name":"Journal of Symbolic Logic","issn_l":"0022-4812","issn":["0022-4812","1943-5886"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Symbolic Logic","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5108217091","display_name":"Charles Morgan","orcid":null},"institutions":[{"id":"https://openalex.org/I45129253","display_name":"University College London","ror":"https://ror.org/02jx3x895","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I45129253"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Charles Morgan","raw_affiliation_strings":["Department of Mathematics, University College London, Gower Street, London WC1E 6BT, England E-mail:","Department of Mathematics, University College London, Gower Street, London WC1E 6BT, England E-mail: charles.morgan@ucl.ac.uk"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University College London, Gower Street, London WC1E 6BT, England E-mail:","institution_ids":["https://openalex.org/I45129253"]},{"raw_affiliation_string":"Department of Mathematics, University College London, Gower Street, London WC1E 6BT, England E-mail: charles.morgan@ucl.ac.uk","institution_ids":["https://openalex.org/I45129253"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5108217091"],"corresponding_institution_ids":["https://openalex.org/I45129253"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.24167324,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"63","issue":"3","first_page":"753","last_page":"787"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11703","display_name":"Rings, Modules, and Algebras","score":0.9883000254631042,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T13400","display_name":"Mathematical and Theoretical Analysis","score":0.9840999841690063,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/uncountable-set","display_name":"Uncountable set","score":0.7389987707138062},{"id":"https://openalex.org/keywords/converse","display_name":"Converse","score":0.6598220467567444},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.41749274730682373},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.3565974235534668},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3248329162597656},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09965303540229797},{"id":"https://openalex.org/keywords/countable-set","display_name":"Countable set","score":0.03966653347015381}],"concepts":[{"id":"https://openalex.org/C142399903","wikidata":"https://www.wikidata.org/wiki/Q1128796","display_name":"Uncountable set","level":3,"score":0.7389987707138062},{"id":"https://openalex.org/C2776809875","wikidata":"https://www.wikidata.org/wiki/Q1375963","display_name":"Converse","level":2,"score":0.6598220467567444},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.41749274730682373},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.3565974235534668},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3248329162597656},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09965303540229797},{"id":"https://openalex.org/C110729354","wikidata":"https://www.wikidata.org/wiki/Q185478","display_name":"Countable set","level":2,"score":0.03966653347015381}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.2307/2586711","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2586711","pdf_url":null,"source":{"id":"https://openalex.org/S177675236","display_name":"Journal of Symbolic Logic","issn_l":"0022-4812","issn":["0022-4812","1943-5886"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Symbolic Logic","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.jsl/1183745565","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1183745565","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":7,"referenced_works":["https://openalex.org/W568910110","https://openalex.org/W630314124","https://openalex.org/W1985455938","https://openalex.org/W2611024016","https://openalex.org/W2990586356","https://openalex.org/W4211247031","https://openalex.org/W4247372698"],"related_works":["https://openalex.org/W2100222222","https://openalex.org/W2387449261","https://openalex.org/W2256572025","https://openalex.org/W1982069151","https://openalex.org/W4303646992","https://openalex.org/W2952146172","https://openalex.org/W4300882518","https://openalex.org/W2018852434","https://openalex.org/W2418518962","https://openalex.org/W74109373"],"abstract_inverted_index":{"Abstract":[0],"This":[1],"paper":[2,100],"concerns":[3],"the":[4,9,28,103],"theory":[5],"of":[6,105],"morasses.":[7],"In":[8,27,98],"early":[10,29],"1970s":[11],"Jensen":[12,75],"defined":[13,32,68],"(k,":[14],"\u03b1)-morasses":[15],"for":[16,38],"uncountable":[17],"regular":[18,40],"cardinals":[19,41],"k":[20,25,34,42,51,62,70,86,94,115,124],"and":[21,56,74],"ordinals":[22],"\u03b1":[23],"<":[24],".":[26,43],"1980s":[30],"Velleman":[31],"(":[33,50,61,69,85,93,114,123],",":[35,52,63,71,87,95,116,125],"1)-simplified":[36,53],"morasses":[37,73],"all":[39],"He":[44],"showed":[45],"that":[46,80,109],"there":[47,59,82,90,111,120],"is":[48,60,83,91,112,121],"a":[49,84,92,113,122],"morass":[54,118],"if":[55,58,81,110],"only":[57],"1)-morass.":[64],"More":[65],"recently":[66],"he":[67],"2)-simplified":[72,96,117],"was":[76],"able":[77],"to":[78],"show":[79],"2)-morass":[88],"then":[89,119],"morass.":[97],"this":[99],"we":[101],"prove":[102],"converse":[104],"Jensen's":[106],"result,":[107],"i.e.,":[108],"2)-morass.":[126]},"counts_by_year":[{"year":2017,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}