{"id":"https://openalex.org/W2750547443","doi":"https://doi.org/10.1002/malq.202100028","title":"Product cones in dense pairs","display_name":"Product cones in dense pairs","publication_year":2022,"publication_date":"2022-01-21","ids":{"openalex":"https://openalex.org/W2750547443","doi":"https://doi.org/10.1002/malq.202100028","mag":"2750547443"},"language":"en","primary_location":{"id":"doi:10.1002/malq.202100028","is_oa":true,"landing_page_url":"https://doi.org/10.1002/malq.202100028","pdf_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1002/malq.202100028","source":{"id":"https://openalex.org/S172351290","display_name":"Mathematical logic quarterly","issn_l":"0044-3050","issn":["0044-3050","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Logic Quarterly","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1002/malq.202100028","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5014788972","display_name":"Pantelis E. Eleftheriou","orcid":"https://orcid.org/0000-0003-0687-1096"},"institutions":[{"id":"https://openalex.org/I130828816","display_name":"University of Leeds","ror":"https://ror.org/024mrxd33","country_code":"GB","type":"education","lineage":["https://openalex.org/I130828816"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Pantelis E. Eleftheriou","raw_affiliation_strings":["School of Mathematics University of Leeds Leeds LS2 9JT United Kingdom"],"raw_orcid":"https://orcid.org/0000-0003-0687-1096","affiliations":[{"raw_affiliation_string":"School of Mathematics University of Leeds Leeds LS2 9JT United Kingdom","institution_ids":["https://openalex.org/I130828816"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5014788972"],"corresponding_institution_ids":["https://openalex.org/I130828816"],"apc_list":{"value":2630,"currency":"USD","value_usd":2630},"apc_paid":{"value":2630,"currency":"USD","value_usd":2630},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00299828,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"68","issue":"3","first_page":"279","last_page":"287"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":1.0,"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":1.0,"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":0.9961000084877014,"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":0.9945999979972839,"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/product","display_name":"Product (mathematics)","score":0.8039954900741577},{"id":"https://openalex.org/keywords/cone","display_name":"Cone (formal languages)","score":0.6272025108337402},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6238484978675842},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6164310574531555},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.5602968335151672},{"id":"https://openalex.org/keywords/decomposition","display_name":"Decomposition","score":0.5533843636512756},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.418889582157135},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.4100106954574585},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.25456055998802185},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1651831567287445},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.0754634439945221},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.047162026166915894},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.034494876861572266}],"concepts":[{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.8039954900741577},{"id":"https://openalex.org/C30014739","wikidata":"https://www.wikidata.org/wiki/Q5159445","display_name":"Cone (formal languages)","level":2,"score":0.6272025108337402},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6238484978675842},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6164310574531555},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.5602968335151672},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.5533843636512756},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.418889582157135},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.4100106954574585},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.25456055998802185},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1651831567287445},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0754634439945221},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.047162026166915894},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.034494876861572266},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","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":5,"locations":[{"id":"doi:10.1002/malq.202100028","is_oa":true,"landing_page_url":"https://doi.org/10.1002/malq.202100028","pdf_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1002/malq.202100028","source":{"id":"https://openalex.org/S172351290","display_name":"Mathematical logic quarterly","issn_l":"0044-3050","issn":["0044-3050","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Logic Quarterly","raw_type":"journal-article"},{"id":"pmh:oai:eprints.whiterose.ac.uk:202293","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306400854","display_name":"White Rose Research Online (University of Leeds, The University of Sheffield, University of York)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2800616092","host_organization_name":"White Rose University Consortium","host_organization_lineage":["https://openalex.org/I2800616092"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"pmh:oai:arXiv.org:1708.03894","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1708.03894","pdf_url":"https://arxiv.org/pdf/1708.03894","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":null,"raw_type":"text"},{"id":"mag:2750547443","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1708.03894","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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.1708.03894","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1708.03894","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"Preprint"}],"best_oa_location":{"id":"doi:10.1002/malq.202100028","is_oa":true,"landing_page_url":"https://doi.org/10.1002/malq.202100028","pdf_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1002/malq.202100028","source":{"id":"https://openalex.org/S172351290","display_name":"Mathematical logic quarterly","issn_l":"0044-3050","issn":["0044-3050","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Logic Quarterly","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4216255205","display_name":null,"funder_award_id":"EP/V003291/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G672739136","display_name":"Model Theory, Diophantine Geometry and Combinatorics","funder_award_id":"EP/V003291/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2750547443.pdf","grobid_xml":"https://content.openalex.org/works/W2750547443.grobid-xml"},"referenced_works_count":15,"referenced_works":["https://openalex.org/W250940406","https://openalex.org/W1590316766","https://openalex.org/W1974917092","https://openalex.org/W1976100776","https://openalex.org/W2017911566","https://openalex.org/W2065070707","https://openalex.org/W2066256748","https://openalex.org/W2072040502","https://openalex.org/W2085118832","https://openalex.org/W2088709272","https://openalex.org/W2096219423","https://openalex.org/W2144694995","https://openalex.org/W2171286238","https://openalex.org/W2342806294","https://openalex.org/W3082499975"],"related_works":["https://openalex.org/W2608283193","https://openalex.org/W2746451277","https://openalex.org/W2899708520","https://openalex.org/W3101493318","https://openalex.org/W3134016517","https://openalex.org/W1982244490","https://openalex.org/W3124842481","https://openalex.org/W167283838","https://openalex.org/W2063036605","https://openalex.org/W2916417859","https://openalex.org/W2021363186","https://openalex.org/W1979825551","https://openalex.org/W2055807387","https://openalex.org/W2019597370","https://openalex.org/W1970985230","https://openalex.org/W2811224401","https://openalex.org/W1600006814","https://openalex.org/W2000466669","https://openalex.org/W3112080192","https://openalex.org/W2323733351"],"abstract_inverted_index":{"Abstract":[0],"Let":[1],"be":[2],"an":[3,7],"o\u2010minimal":[4],"expansion":[5],"of":[6,24],"ordered":[8],"group,":[9],"and":[10,30],"a":[11,25,34,40,55],"dense":[12],"set":[13],"such":[14],"that":[15],"certain":[16],"tameness":[17],"conditions":[18],"hold.":[19],"We":[20],"introduce":[21],"the":[22],"notion":[23],"product":[26,41],"cone":[27,42],"in":[28],",":[29],"prove:":[31],"if":[32],"expands":[33],"real":[35],"closed":[36],"field,":[37],"then":[38,47],"admits":[39],"decomposition.":[43],"If":[44],"is":[45],"linear,":[46],"it":[48],"does":[49],"not.":[50],"In":[51],"particular,":[52],"we":[53],"settle":[54],"question":[56],"from":[57],"[10].":[58]},"counts_by_year":[],"updated_date":"2026-08-08T01:25:22.217667","created_date":"2025-10-10T00:00:00"}
