{"id":"https://openalex.org/W2890239988","doi":"https://doi.org/10.2178/jsl/1082418541","title":"Ladder gaps over stationary sets","display_name":"Ladder gaps over stationary sets","publication_year":2004,"publication_date":"2004-06-01","ids":{"openalex":"https://openalex.org/W2890239988","doi":"https://doi.org/10.2178/jsl/1082418541","mag":"2890239988"},"language":"en","primary_location":{"id":"doi:10.2178/jsl/1082418541","is_oa":true,"landing_page_url":"https://doi.org/10.2178/jsl/1082418541","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/2BEAFB9173E6EC2746389F666A9DC857/S002248120000788Xa.pdf/div-class-title-ladder-gaps-over-stationary-sets-div.pdf","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":true,"oa_status":"bronze","oa_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/2BEAFB9173E6EC2746389F666A9DC857/S002248120000788Xa.pdf/div-class-title-ladder-gaps-over-stationary-sets-div.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5050549524","display_name":"Uri Abraham","orcid":null},"institutions":[{"id":"https://openalex.org/I124227911","display_name":"Ben-Gurion University of the Negev","ror":"https://ror.org/05tkyf982","country_code":"IL","type":"education","lineage":["https://openalex.org/I124227911"]},{"id":"https://openalex.org/I197251160","display_name":"Hebrew University of Jerusalem","ror":"https://ror.org/03qxff017","country_code":"IL","type":"education","lineage":["https://openalex.org/I197251160"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Uri Abraham","raw_affiliation_strings":["Department of Mathematics, Ben-Gurion University, Be\u00e9r-Sheva, 84105, Israel, E-mail:","Departments of Mathematics and Computer Science, Ben-Gurion University, Be\u00e9r-Sheva, Israel","Institute of Mathematics The Hebrew University, Jerusalem, Israel"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Ben-Gurion University, Be\u00e9r-Sheva, 84105, Israel, E-mail:","institution_ids":["https://openalex.org/I124227911"]},{"raw_affiliation_string":"Departments of Mathematics and Computer Science, Ben-Gurion University, Be\u00e9r-Sheva, Israel","institution_ids":["https://openalex.org/I124227911"]},{"raw_affiliation_string":"Institute of Mathematics The Hebrew University, Jerusalem, Israel","institution_ids":["https://openalex.org/I197251160"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5024923217","display_name":"Saharon Shelah","orcid":"https://orcid.org/0000-0003-0462-3152"},"institutions":[{"id":"https://openalex.org/I124227911","display_name":"Ben-Gurion University of the Negev","ror":"https://ror.org/05tkyf982","country_code":"IL","type":"education","lineage":["https://openalex.org/I124227911"]},{"id":"https://openalex.org/I197251160","display_name":"Hebrew University of Jerusalem","ror":"https://ror.org/03qxff017","country_code":"IL","type":"education","lineage":["https://openalex.org/I197251160"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Saharon Shelah","raw_affiliation_strings":["Institute of Mathematics, The Hebrew University, Jerusalem, Israel, E-mail:","Departments of Mathematics and Computer Science, Ben-Gurion University, Be\u00e9r-Sheva, Israel","Institute of Mathematics The Hebrew University, Jerusalem, Israel"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Mathematics, The Hebrew University, Jerusalem, Israel, E-mail:","institution_ids":["https://openalex.org/I197251160"]},{"raw_affiliation_string":"Departments of Mathematics and Computer Science, Ben-Gurion University, Be\u00e9r-Sheva, Israel","institution_ids":["https://openalex.org/I124227911"]},{"raw_affiliation_string":"Institute of Mathematics The Hebrew University, Jerusalem, Israel","institution_ids":["https://openalex.org/I197251160"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.39,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.6420394,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"69","issue":"2","first_page":"518","last_page":"532"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9975000023841858,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.9835000038146973,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/hausdorff-space","display_name":"Hausdorff space","score":0.7088128924369812},{"id":"https://openalex.org/keywords/chain","display_name":"Chain (unit)","score":0.6888149976730347},{"id":"https://openalex.org/keywords/partially-ordered-set","display_name":"Partially ordered set","score":0.6752331852912903},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6549835205078125},{"id":"https://openalex.org/keywords/forcing","display_name":"Forcing (mathematics)","score":0.6396206617355347},{"id":"https://openalex.org/keywords/hausdorff-distance","display_name":"Hausdorff distance","score":0.6097291111946106},{"id":"https://openalex.org/keywords/hausdorff-dimension","display_name":"Hausdorff dimension","score":0.5729061961174011},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.5533668994903564},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5477879643440247},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.45709484815597534},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4078856110572815},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3863493800163269},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.23205888271331787},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.23056936264038086},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.12012264132499695},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.11122521758079529}],"concepts":[{"id":"https://openalex.org/C191399826","wikidata":"https://www.wikidata.org/wiki/Q326908","display_name":"Hausdorff space","level":2,"score":0.7088128924369812},{"id":"https://openalex.org/C199185054","wikidata":"https://www.wikidata.org/wiki/Q552299","display_name":"Chain (unit)","level":2,"score":0.6888149976730347},{"id":"https://openalex.org/C180645754","wikidata":"https://www.wikidata.org/wiki/Q474715","display_name":"Partially ordered set","level":2,"score":0.6752331852912903},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6549835205078125},{"id":"https://openalex.org/C197115733","wikidata":"https://www.wikidata.org/wiki/Q1003136","display_name":"Forcing (mathematics)","level":2,"score":0.6396206617355347},{"id":"https://openalex.org/C141898687","wikidata":"https://www.wikidata.org/wiki/Q1501997","display_name":"Hausdorff distance","level":2,"score":0.6097291111946106},{"id":"https://openalex.org/C194198291","wikidata":"https://www.wikidata.org/wiki/Q565186","display_name":"Hausdorff dimension","level":2,"score":0.5729061961174011},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.5533668994903564},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5477879643440247},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.45709484815597534},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4078856110572815},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3863493800163269},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.23205888271331787},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.23056936264038086},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.12012264132499695},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.11122521758079529},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.2178/jsl/1082418541","is_oa":true,"landing_page_url":"https://doi.org/10.2178/jsl/1082418541","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/2BEAFB9173E6EC2746389F666A9DC857/S002248120000788Xa.pdf/div-class-title-ladder-gaps-over-stationary-sets-div.pdf","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:CiteSeerX.psu:10.1.1.205.2425","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.205.2425","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://shelah.logic.at/files/598.pdf","raw_type":"text"},{"id":"pmh:oai:CULeuclid:euclid.jsl/1082418541","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1082418541","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":{"id":"doi:10.2178/jsl/1082418541","is_oa":true,"landing_page_url":"https://doi.org/10.2178/jsl/1082418541","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/2BEAFB9173E6EC2746389F666A9DC857/S002248120000788Xa.pdf/div-class-title-ladder-gaps-over-stationary-sets-div.pdf","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"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2890239988.pdf","grobid_xml":"https://content.openalex.org/works/W2890239988.grobid-xml"},"referenced_works_count":3,"referenced_works":["https://openalex.org/W1970364998","https://openalex.org/W2034946468","https://openalex.org/W2088829096"],"related_works":["https://openalex.org/W2106070061","https://openalex.org/W4390961156","https://openalex.org/W1963087247","https://openalex.org/W4312224320","https://openalex.org/W2347443236","https://openalex.org/W2886349793","https://openalex.org/W2962824122","https://openalex.org/W1144450175","https://openalex.org/W1512585147","https://openalex.org/W1991371429"],"abstract_inverted_index":{"Abstract.":[0],"For":[1],"a":[2,11,18,32,55,73,108],"stationary":[3,41],"set":[4,42],"S":[5,16,43,50,70],"\u2286":[6],"\u03c9":[7,67],"1":[8,68],",":[9,17,44,51],"and":[10,28],"ladder":[12,47,64],"system":[13],"C":[14,24,48,59],"over":[15,49,66],"new":[19,83],"type":[20,84],"of":[21,35,85,102],"gaps":[22],"called":[23,88],"-Hausdorff":[25],"is":[26,58,79,92,106],"introduced":[27],"investigated.":[29],"We":[30,94],"describe":[31],"forcing":[33],"model":[34],"ZFC":[36],"in":[37],"which,":[38],"for":[39,45,62],"some":[40],"every":[46,52,63],"gap":[53,74],"contains":[54],"subgap":[56,77],"that":[57,78,96],"-Hausdorff.":[60,81],"But":[61],"E":[65,80],"\u2216":[69],"there":[71],"exists":[72],"with":[75,99],"no":[76],"A":[82],"chain":[86,90],"condition,":[87,91],"polarized":[89,103,109],"introduced.":[93],"prove":[95],"the":[97],"iteration":[98],"finite":[100],"support":[101],"c.c.c.":[104,110],"posets":[105],"again":[107],"poset.":[111]},"counts_by_year":[{"year":2022,"cited_by_count":1}],"updated_date":"2026-08-11T07:18:39.950985","created_date":"2025-10-10T00:00:00"}