{"id":"https://openalex.org/W7214766204","doi":"https://doi.org/10.48550/arxiv.2609.34068","title":"Borel complexity for product of trees and commuting partial maps","display_name":"Borel complexity for product of trees and commuting partial maps","publication_year":2026,"publication_date":"2026-09-28","ids":{"openalex":"https://openalex.org/W7214766204","doi":"https://doi.org/10.48550/arxiv.2609.34068"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.34068","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.34068","pdf_url":"https://arxiv.org/pdf/2609.34068","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,"listed_in":[],"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"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.34068","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5077192594","display_name":"Koichi Oyakawa","orcid":"https://orcid.org/0000-0003-0441-4553","observed_orcids":["https://orcid.org/0000-0003-0441-4553"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Oyakawa, Koichi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5077192594"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"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":0.673799991607666,"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":0.673799991607666,"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.11169999837875366,"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/T10304","display_name":"Geometric and Algebraic Topology","score":0.08780000358819962,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/borel-complexity","display_name":"Borel complexity","score":0.921999990940094},{"id":"https://openalex.org/keywords/acylindrical-actions","display_name":"acylindrical actions","score":0.8429999947547913},{"id":"https://openalex.org/keywords/countable-borel-equivalence-relations","display_name":"countable Borel equivalence relations","score":0.9229999780654907},{"id":"https://openalex.org/keywords/standard-borel-spaces","display_name":"standard Borel spaces","score":0.824999988079071},{"id":"https://openalex.org/keywords/commutative-monoids","display_name":"commutative monoids","score":0.8059999942779541}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9126999974250793},{"id":"https://openalex.org/C5278979","wikidata":"https://www.wikidata.org/wiki/Q4944905","display_name":"Borel equivalence relation","level":4,"score":0.8572999835014343},{"id":"https://openalex.org/C119238805","wikidata":"https://www.wikidata.org/wiki/Q229102","display_name":"Surjective function","level":2,"score":0.7146000266075134},{"id":"https://openalex.org/C156103551","wikidata":"https://www.wikidata.org/wiki/Q130998","display_name":"Equivalence relation","level":2,"score":0.6376000046730042},{"id":"https://openalex.org/C162362422","wikidata":"https://www.wikidata.org/wiki/Q1363919","display_name":"Second-countable space","level":3,"score":0.545199990272522},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.5148000121116638},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.5127999782562256},{"id":"https://openalex.org/C31316033","wikidata":"https://www.wikidata.org/wiki/Q1207972","display_name":"Polish space","level":3,"score":0.48919999599456787},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.47749999165534973},{"id":"https://openalex.org/C110729354","wikidata":"https://www.wikidata.org/wiki/Q185478","display_name":"Countable set","level":2,"score":0.46399998664855957},{"id":"https://openalex.org/C25942563","wikidata":"https://www.wikidata.org/wiki/Q893487","display_name":"Borel hierarchy","level":4,"score":0.44600000977516174},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4345000088214874},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.41179999709129333},{"id":"https://openalex.org/C39952206","wikidata":"https://www.wikidata.org/wiki/Q21086747","display_name":"Borel set","level":2,"score":0.39730000495910645},{"id":"https://openalex.org/C183778304","wikidata":"https://www.wikidata.org/wiki/Q165474","display_name":"Commutative property","level":2,"score":0.38440001010894775},{"id":"https://openalex.org/C2780791683","wikidata":"https://www.wikidata.org/wiki/Q846785","display_name":"Action (physics)","level":2,"score":0.38440001010894775},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.37279999256134033},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3409000039100647},{"id":"https://openalex.org/C12871628","wikidata":"https://www.wikidata.org/wiki/Q7598372","display_name":"Standard probability space","level":2,"score":0.31679999828338623},{"id":"https://openalex.org/C48659774","wikidata":"https://www.wikidata.org/wiki/Q4907197","display_name":"Bijection, injection and surjection","level":3,"score":0.3165999948978424},{"id":"https://openalex.org/C65180967","wikidata":"https://www.wikidata.org/wiki/Q130901","display_name":"Binary relation","level":2,"score":0.29840001463890076},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.29010000824928284},{"id":"https://openalex.org/C137212723","wikidata":"https://www.wikidata.org/wiki/Q1948412","display_name":"Morphism","level":2,"score":0.28870001435279846},{"id":"https://openalex.org/C21031990","wikidata":"https://www.wikidata.org/wiki/Q355020","display_name":"Probability measure","level":2,"score":0.28119999170303345},{"id":"https://openalex.org/C123222754","wikidata":"https://www.wikidata.org/wiki/Q1070472","display_name":"Product topology","level":2,"score":0.263700008392334}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.34068","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.34068","pdf_url":"https://arxiv.org/pdf/2609.34068","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,"listed_in":[],"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":"doi:10.48550/arxiv.2609.34068","doi":"https://doi.org/10.48550/arxiv.2609.34068","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.34068","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,"listed_in":[],"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":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.34068","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.34068","pdf_url":"https://arxiv.org/pdf/2609.34068","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,"listed_in":[],"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"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214766204.pdf","grobid_xml":"https://content.openalex.org/works/W7214766204.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W4415199972"],"related_works":["https://openalex.org/W3105609498","https://openalex.org/W4394948724","https://openalex.org/W7203924017","https://openalex.org/W7101180284","https://openalex.org/W7097192919","https://openalex.org/W2162542096","https://openalex.org/W2596649951","https://openalex.org/W2095437644","https://openalex.org/W7131663759","https://openalex.org/W2144184882"],"abstract_inverted_index":{"We":[0],"prove":[1],"that":[2,43],"every":[3],"acylindrical":[4],"action":[5],"on":[6,19,56],"uniformly":[7],"locally":[8],"finite":[9],"product":[10],"of":[11,30,58,61],"trees":[12],"induces":[13],"the":[14,20],"hyperfinite":[15],"orbit":[16],"equivalence":[17,49],"relation":[18],"Roller":[21],"boundary.":[22],"As":[23],"a":[24,31,45],"byproduct,":[25],"we":[26],"construct":[27],"an":[28],"example":[29],"standard":[32],"Borel":[33,41,48],"space":[34],"and":[35],"two":[36],"commuting":[37],"bounded-to-one":[38,59],"surjective":[39],"partial":[40],"maps":[42],"generate":[44],"universal":[46],"countable":[47],"relation.":[50],"This":[51],"contrasts":[52],"to":[53],"Shinko-Weilacher-Yu's":[54],"theorem":[55],"hyperfiniteness":[57],"actions":[60],"commutative":[62],"monoids.":[63]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-30T00:00:00"}
