{"id":"https://openalex.org/W3160938664","doi":"https://doi.org/10.1142/s0219061322500283","title":"Actions of tame abelian product groups","display_name":"Actions of tame abelian product groups","publication_year":2022,"publication_date":"2022-11-09","ids":{"openalex":"https://openalex.org/W3160938664","doi":"https://doi.org/10.1142/s0219061322500283","mag":"3160938664"},"language":"en","primary_location":{"id":"doi:10.1142/s0219061322500283","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0219061322500283","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/A5005341590","display_name":"Shaun Allison","orcid":null},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Shaun Allison","raw_affiliation_strings":["Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA 15213, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA 15213, USA","institution_ids":["https://openalex.org/I74973139"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5015845391","display_name":"Assaf Shani","orcid":"https://orcid.org/0000-0002-8357-8910"},"institutions":[{"id":"https://openalex.org/I136199984","display_name":"Harvard University","ror":"https://ror.org/03vek6s52","country_code":"US","type":"education","lineage":["https://openalex.org/I136199984"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Assaf Shani","raw_affiliation_strings":["Department of Mathematics, Harvard University, Cambridge, MA 02138, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Harvard University, Cambridge, MA 02138, USA","institution_ids":["https://openalex.org/I136199984"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5015845391"],"corresponding_institution_ids":["https://openalex.org/I136199984"],"apc_list":null,"apc_paid":null,"fwci":0.3919,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.50670533,"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/T11151","display_name":"Advanced Topology and Set Theory","score":0.9995999932289124,"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":0.9995999932289124,"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":0.9994000196456909,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.991100013256073,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/abelian-group","display_name":"Abelian group","score":0.8354141712188721},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7980887293815613},{"id":"https://openalex.org/keywords/equivalence-relation","display_name":"Equivalence relation","score":0.7747471332550049},{"id":"https://openalex.org/keywords/countable-set","display_name":"Countable set","score":0.5747146010398865},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4936572015285492},{"id":"https://openalex.org/keywords/group-action","display_name":"Group action","score":0.47068077325820923},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.46152299642562866},{"id":"https://openalex.org/keywords/polish-space","display_name":"Polish space","score":0.4459131062030792},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3974747061729431},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3584359884262085},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.35811012983322144},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.06135198473930359}],"concepts":[{"id":"https://openalex.org/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.8354141712188721},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7980887293815613},{"id":"https://openalex.org/C156103551","wikidata":"https://www.wikidata.org/wiki/Q130998","display_name":"Equivalence relation","level":2,"score":0.7747471332550049},{"id":"https://openalex.org/C110729354","wikidata":"https://www.wikidata.org/wiki/Q185478","display_name":"Countable set","level":2,"score":0.5747146010398865},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4936572015285492},{"id":"https://openalex.org/C131715654","wikidata":"https://www.wikidata.org/wiki/Q288465","display_name":"Group action","level":3,"score":0.47068077325820923},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.46152299642562866},{"id":"https://openalex.org/C31316033","wikidata":"https://www.wikidata.org/wiki/Q1207972","display_name":"Polish space","level":3,"score":0.4459131062030792},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3974747061729431},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3584359884262085},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.35811012983322144},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.06135198473930359},{"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/C70710897","wikidata":"https://www.wikidata.org/wiki/Q680081","display_name":"Separable space","level":2,"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/s0219061322500283","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0219061322500283","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W19898668","https://openalex.org/W633446433","https://openalex.org/W976787978","https://openalex.org/W1488189778","https://openalex.org/W1502526905","https://openalex.org/W1510713123","https://openalex.org/W1539382740","https://openalex.org/W1602868010","https://openalex.org/W2024078235","https://openalex.org/W2030711895","https://openalex.org/W2032982436","https://openalex.org/W2074533872","https://openalex.org/W2115456387","https://openalex.org/W2152657121","https://openalex.org/W2897833235","https://openalex.org/W2963245506","https://openalex.org/W2980979461","https://openalex.org/W3048702928","https://openalex.org/W3049518724"],"related_works":["https://openalex.org/W1972195264","https://openalex.org/W4311231917","https://openalex.org/W2026504565","https://openalex.org/W4302132510","https://openalex.org/W2963349776","https://openalex.org/W2114381574","https://openalex.org/W2264355049","https://openalex.org/W2139131833","https://openalex.org/W1978325228","https://openalex.org/W2610155317"],"abstract_inverted_index":{"A":[0],"Polish":[1,37,62,144],"group":[2,120],"G":[3,51,121],"is":[4,18,52,109,123,189],"tame":[5,200],"if":[6],"for":[7,24,49,77,193,217],"any":[8],"continuous":[9],"action":[10,116],"of":[11,36,117,136,166,176,197,199,211,219],"G,":[12,79],"the":[13,80,95,106,134,164,177,190,194],"corresponding":[14],"orbit":[15,81],"equivalence":[16,82,171],"relation":[17,83],"Borel.":[19],"When":[20],"[Formula:":[21,27,89,100,110,126],"see":[22,28,90,101,111,127],"text]":[23,112],"countable":[25],"abelian":[26,61,143,201],"text],":[29,91,128],"Solecki":[30],"[Equivalence":[31],"relations":[32,172],"induced":[33,173],"by":[34,113,174],"actions":[35,175,198],"groups,":[38],"Trans.":[39],"Amer.":[40],"Math.":[41,68,150],"Soc.":[42],"347":[43],"(1995)":[44],"4765\u20134777]":[45],"gave":[46],"a":[47,119],"characterization":[48],"when":[50],"tame.":[53],"In":[54],"[L.":[55,137],"Ding":[56,72,138],"and":[57,64,73,129,139,146],"S.":[58,140],"Gao,":[59,141],"Non-archimedean":[60,142],"groups":[63,145],"their":[65,147],"actions,":[66,148],"Adv.":[67,149],"307":[69,151],"(2017)":[70,152],"312\u2013343],":[71],"Gao":[74],"showed":[75],"that":[76,94,105,187],"such":[78,118],"must":[84],"in":[85],"fact":[86],"be":[87,99],"potentially":[88,125],"while":[92],"conjecturing":[93],"optimal":[96,107,191],"bound":[97,108,192],"could":[98],"text].":[102],"We":[103],"show":[104,130],"constructing":[114],"an":[115],"which":[122],"not":[124],"how":[131],"to":[132,154],"modify":[133],"analysis":[135,206],"312\u2013343]":[153],"get":[155],"this":[156,188],"slightly":[157],"better":[158],"upper":[159],"bound.":[160],"It":[161],"follows,":[162],"using":[163],"results":[165],"Hjorth":[167],"et":[168],"al.":[169],"[Borel":[170],"symmetric":[178],"group,":[179],"Ann.":[180],"Pure":[181],"Appl.":[182],"Logic":[183],"92":[184],"(1998)":[185],"63\u2013112],":[186],"potential":[195],"complexity":[196],"product":[202],"groups.":[203],"Our":[204],"lower-bound":[205],"involves":[207],"forcing":[208],"over":[209],"models":[210],"set":[212],"theory":[213],"where":[214],"choice":[215],"fails":[216],"sequences":[218],"finite":[220],"sets.":[221]},"counts_by_year":[{"year":2022,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
