{"id":"https://openalex.org/W2509708725","doi":"https://doi.org/10.1002/malq.201600009","title":"The strong tree property and weak square","display_name":"The strong tree property and weak square","publication_year":2016,"publication_date":"2016-12-22","ids":{"openalex":"https://openalex.org/W2509708725","doi":"https://doi.org/10.1002/malq.201600009","mag":"2509708725"},"language":"en","primary_location":{"id":"doi:10.1002/malq.201600009","is_oa":false,"landing_page_url":"https://doi.org/10.1002/malq.201600009","pdf_url":null,"source":{"id":"https://openalex.org/S172351290","display_name":"Mathematical logic quarterly","issn_l":"0942-5616","issn":["0942-5616","1521-3870"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Logic Quarterly","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1601.07824","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5072723653","display_name":"Yair Hayut","orcid":"https://orcid.org/0000-0002-3805-7446"},"institutions":[{"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"]},{"id":"https://openalex.org/I4210130028","display_name":"National Library of Israel","ror":"https://ror.org/03be63z97","country_code":"IL","type":"archive","lineage":["https://openalex.org/I4210130028"]}],"countries":["IL"],"is_corresponding":true,"raw_author_name":"Yair Hayut","raw_affiliation_strings":["Einstein Institute of Mathematics Edmond J. Safra Campus, The Hebrew University of Jerusalem Givat Ram Jerusalem 9190401 Israel","Einstein Institute of Mathematics; Edmond J. Safra Campus; The Hebrew University of Jerusalem; Givat Ram Jerusalem 9190401 Israel"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Einstein Institute of Mathematics Edmond J. Safra Campus, The Hebrew University of Jerusalem Givat Ram Jerusalem 9190401 Israel","institution_ids":["https://openalex.org/I197251160","https://openalex.org/I4210130028"]},{"raw_affiliation_string":"Einstein Institute of Mathematics; Edmond J. Safra Campus; The Hebrew University of Jerusalem; Givat Ram Jerusalem 9190401 Israel","institution_ids":["https://openalex.org/I197251160"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5020068591","display_name":"Spencer Unger","orcid":null},"institutions":[{"id":"https://openalex.org/I161318765","display_name":"University of California, Los Angeles","ror":"https://ror.org/046rm7j60","country_code":"US","type":"education","lineage":["https://openalex.org/I161318765"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Spencer Unger","raw_affiliation_strings":["Mathematics Department University of California at Los Angeles Box 951555 Los Angeles CA 90095\u20101555 United States of America"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematics Department University of California at Los Angeles Box 951555 Los Angeles CA 90095\u20101555 United States of America","institution_ids":["https://openalex.org/I161318765"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5020068591","https://openalex.org/A5072723653"],"corresponding_institution_ids":["https://openalex.org/I161318765","https://openalex.org/I197251160","https://openalex.org/I4210130028"],"apc_list":{"value":2630,"currency":"USD","value_usd":2630},"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.1127211,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"63","issue":"1-2","first_page":"150","last_page":"154"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9997000098228455,"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":0.9997000098228455,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9746000170707703,"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"}},{"id":"https://openalex.org/T11703","display_name":"Rings, Modules, and Algebras","score":0.926800012588501,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/aleph","display_name":"Aleph","score":0.9561890363693237},{"id":"https://openalex.org/keywords/omega","display_name":"Omega","score":0.8965693712234497},{"id":"https://openalex.org/keywords/square","display_name":"Square (algebra)","score":0.7121723294258118},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.7015203833580017},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6280100345611572},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.6244820952415466},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.49159297347068787},{"id":"https://openalex.org/keywords/scale","display_name":"Scale (ratio)","score":0.4446994662284851},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.32783451676368713},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2933451533317566},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.13010704517364502},{"id":"https://openalex.org/keywords/particle-physics","display_name":"Particle physics","score":0.1274472177028656},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.07565030455589294},{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.0660894513130188}],"concepts":[{"id":"https://openalex.org/C2781424814","wikidata":"https://www.wikidata.org/wiki/Q15033","display_name":"Aleph","level":2,"score":0.9561890363693237},{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.8965693712234497},{"id":"https://openalex.org/C135692309","wikidata":"https://www.wikidata.org/wiki/Q111124","display_name":"Square (algebra)","level":2,"score":0.7121723294258118},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.7015203833580017},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6280100345611572},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.6244820952415466},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.49159297347068787},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.4446994662284851},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.32783451676368713},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2933451533317566},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.13010704517364502},{"id":"https://openalex.org/C109214941","wikidata":"https://www.wikidata.org/wiki/Q18334","display_name":"Particle physics","level":1,"score":0.1274472177028656},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.07565030455589294},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0660894513130188},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1002/malq.201600009","is_oa":false,"landing_page_url":"https://doi.org/10.1002/malq.201600009","pdf_url":null,"source":{"id":"https://openalex.org/S172351290","display_name":"Mathematical logic quarterly","issn_l":"0942-5616","issn":["0942-5616","1521-3870"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Logic Quarterly","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1601.07824","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1601.07824","pdf_url":"https://arxiv.org/pdf/1601.07824","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"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"},{"id":"mag:2509708725","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1601.07824.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"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":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1601.07824","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1601.07824","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1601.07824","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1601.07824","pdf_url":"https://arxiv.org/pdf/1601.07824","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"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"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2509708725.pdf","grobid_xml":"https://content.openalex.org/works/W2509708725.grobid-xml"},"referenced_works_count":10,"referenced_works":["https://openalex.org/W1143798487","https://openalex.org/W2004159708","https://openalex.org/W2023911024","https://openalex.org/W2040632702","https://openalex.org/W2066172220","https://openalex.org/W2071085691","https://openalex.org/W2074199159","https://openalex.org/W2092835503","https://openalex.org/W2122092051","https://openalex.org/W6838143816"],"related_works":["https://openalex.org/W2963419477","https://openalex.org/W2887360181","https://openalex.org/W2977305452","https://openalex.org/W2404991367","https://openalex.org/W2954957365","https://openalex.org/W2806408298","https://openalex.org/W1603710866","https://openalex.org/W2606860161","https://openalex.org/W2951939129","https://openalex.org/W2212158770","https://openalex.org/W2216969168","https://openalex.org/W2121150916","https://openalex.org/W2793788120","https://openalex.org/W2951972304","https://openalex.org/W2908592207","https://openalex.org/W2951176201","https://openalex.org/W3149729538","https://openalex.org/W2952379986","https://openalex.org/W2952494000","https://openalex.org/W2949653698"],"abstract_inverted_index":{"We":[0],"show":[1],"that":[2,12],"it":[3],"is":[4],"consistent,":[5],"relative":[6],"to":[7],"\u03c9":[8],"many":[9],"supercompact":[10],"cardinals,":[11],"the":[13],"super":[14],"tree":[15],"property":[16],"holds":[17],"at":[18,31],"for":[19],"all":[20],"but":[21],"there":[22],"are":[23],"weak":[24],"square":[25],"and":[26],"a":[27],"very":[28],"good":[29],"scale":[30],".":[32]},"counts_by_year":[],"updated_date":"2026-05-21T09:19:25.381259","created_date":"2025-10-10T00:00:00"}