{"id":"https://openalex.org/W2946335497","doi":"https://doi.org/10.1142/s0219061322500301","title":"Co-theory of sorted profinite groups for PAC structures","display_name":"Co-theory of sorted profinite groups for PAC structures","publication_year":2022,"publication_date":"2022-11-09","ids":{"openalex":"https://openalex.org/W2946335497","doi":"https://doi.org/10.1142/s0219061322500301","mag":"2946335497"},"language":"en","primary_location":{"id":"doi:10.1142/s0219061322500301","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0219061322500301","pdf_url":null,"source":{"id":"https://openalex.org/S29890666","display_name":"Journal of Mathematical Logic","issn_l":"0219-0613","issn":["0219-0613","1793-6691"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Mathematical 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/A5073653212","display_name":"Daniel Max Hoffmann","orcid":"https://orcid.org/0000-0002-4514-269X"},"institutions":[{"id":"https://openalex.org/I4654613","display_name":"University of Warsaw","ror":"https://ror.org/039bjqg32","country_code":"PL","type":"education","lineage":["https://openalex.org/I4654613"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Daniel Max Hoffmann","raw_affiliation_strings":["Instytut Matematyki, Uniwersytet Warszawski, Warszawa, Poland"],"affiliations":[{"raw_affiliation_string":"Instytut Matematyki, Uniwersytet Warszawski, Warszawa, Poland","institution_ids":["https://openalex.org/I4654613"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5066235885","display_name":"Junguk Lee","orcid":"https://orcid.org/0000-0002-2150-6145"},"institutions":[{"id":"https://openalex.org/I125608817","display_name":"Korea Institute for Advanced Study","ror":"https://ror.org/041hz9568","country_code":"KR","type":"facility","lineage":["https://openalex.org/I125608817"]}],"countries":["KR"],"is_corresponding":true,"raw_author_name":"Junguk Lee","raw_affiliation_strings":["Center for Mathematical Challenges, Korea Institute for Advanced Study, 85 Hoegiro, Dongdaemun-gu, 02455 Seoul, South Korea"],"affiliations":[{"raw_affiliation_string":"Center for Mathematical Challenges, Korea Institute for Advanced Study, 85 Hoegiro, Dongdaemun-gu, 02455 Seoul, South Korea","institution_ids":["https://openalex.org/I125608817"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5066235885"],"corresponding_institution_ids":["https://openalex.org/I125608817"],"apc_list":null,"apc_paid":null,"fwci":1.2055,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.72807882,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"23","issue":"03","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9994999766349792,"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9994999766349792,"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/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.9994999766349792,"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"}},{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9994999766349792,"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/mathematics","display_name":"Mathematics","score":0.8323467969894409},{"id":"https://openalex.org/keywords/profinite-group","display_name":"Profinite group","score":0.6709260940551758},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.40690502524375916},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3957454264163971},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.21909871697425842}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8323467969894409},{"id":"https://openalex.org/C14735163","wikidata":"https://www.wikidata.org/wiki/Q1428923","display_name":"Profinite group","level":3,"score":0.6709260940551758},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.40690502524375916},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3957454264163971},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.21909871697425842},{"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/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0219061322500301","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0219061322500301","pdf_url":null,"source":{"id":"https://openalex.org/S29890666","display_name":"Journal of Mathematical Logic","issn_l":"0219-0613","issn":["0219-0613","1793-6691"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Mathematical Logic","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":33,"referenced_works":["https://openalex.org/W394295880","https://openalex.org/W615860846","https://openalex.org/W1548944036","https://openalex.org/W1574235262","https://openalex.org/W1870712983","https://openalex.org/W1965513326","https://openalex.org/W1995912769","https://openalex.org/W1996612994","https://openalex.org/W2005659848","https://openalex.org/W2045117194","https://openalex.org/W2067170342","https://openalex.org/W2068475222","https://openalex.org/W2073843573","https://openalex.org/W2092230546","https://openalex.org/W2107559508","https://openalex.org/W2129678180","https://openalex.org/W2327233892","https://openalex.org/W2337728271","https://openalex.org/W2369978792","https://openalex.org/W2593411479","https://openalex.org/W2614564178","https://openalex.org/W2799061192","https://openalex.org/W2806899938","https://openalex.org/W2901759820","https://openalex.org/W2963688969","https://openalex.org/W2963889157","https://openalex.org/W3001155019","https://openalex.org/W3033027137","https://openalex.org/W3087464351","https://openalex.org/W3097517922","https://openalex.org/W3122394183","https://openalex.org/W4246912661","https://openalex.org/W4253001479"],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2200328335","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2911598644"],"abstract_inverted_index":{"We":[0],"achieve":[1],"several":[2,86],"results.":[3],"First,":[4],"we":[5,24,49,77,95],"develop":[6],"a":[7,26],"variant":[8],"of":[9,12,19,33,60],"the":[10,17,51,71,90,97],"theory":[11],"absolute":[13,30],"Galois":[14,31],"groups":[15,32],"in":[16,40,80,100],"context":[18],"many":[20],"sorted":[21],"structures.":[22,102],"Second,":[23],"provide":[25],"method":[27],"for":[28,55],"coding":[29],"structures,":[34],"so":[35],"they":[36],"can":[37],"be":[38],"interpreted":[39],"some":[41],"monster":[42],"model":[43],"with":[44,64],"an":[45,61],"additional":[46],"predicate.":[47],"Third,":[48],"prove":[50],"\u201cWeak":[52],"Independence":[53],"Theorem\u201d":[54],"pseudo-algebraically":[56],"closed":[57],"(PAC)":[58],"substructures":[59,83],"ambient":[62],"structure":[63],"no":[65],"finite":[66],"cover":[67],"property":[68,72],"(nfcp)":[69],"and":[70,84],"[Formula:":[73],"see":[74],"text].":[75],"Fourth,":[76],"describe":[78],"Kim-dividing":[79],"these":[81],"PAC":[82,101],"show":[85],"results":[87],"related":[88],"to":[89],"SOP":[91],"n":[92],"hierarchy.":[93],"Fifth,":[94],"characterize":[96],"algebraic":[98],"closure":[99]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}