{"id":"https://openalex.org/W7220991104","doi":"https://doi.org/10.48550/arxiv.2610.10089","title":"On omega-powers of infinite difference rank","display_name":"On omega-powers of infinite difference rank","publication_year":2026,"publication_date":"2026-10-07","ids":{"openalex":"https://openalex.org/W7220991104","doi":"https://doi.org/10.48550/arxiv.2610.10089"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.10089","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.10089","pdf_url":"https://arxiv.org/pdf/2610.10089","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/2610.10089","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5157895121","display_name":"Maxim Vishnikin","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Vishnikin, Maxim","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5157895121"],"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/T11567","display_name":"semigroups and automata theory","score":0.4684999883174896,"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"}},"topics":[{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.4684999883174896,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.4036000072956085,"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/T11151","display_name":"Advanced Topology and Set Theory","score":0.11219999939203262,"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/open-sets","display_name":"open sets","score":0.8370000123977661},{"id":"https://openalex.org/keywords/descriptive-set-theory","display_name":"descriptive set theory","score":0.6579999923706055},{"id":"https://openalex.org/keywords/infinite-rank","display_name":"infinite rank","score":0.5260000228881836},{"id":"https://openalex.org/keywords/borel-hierarchy","display_name":"Borel hierarchy","score":0.5759999752044678}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7839999794960022},{"id":"https://openalex.org/C31170391","wikidata":"https://www.wikidata.org/wiki/Q188619","display_name":"Hierarchy","level":2,"score":0.6880999803543091},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.6402999758720398},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.44690001010894775},{"id":"https://openalex.org/C176053320","wikidata":"https://www.wikidata.org/wiki/Q2878515","display_name":"Analytical hierarchy","level":3,"score":0.414000004529953},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.36399999260902405},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2881999909877777},{"id":"https://openalex.org/C136979486","wikidata":"https://www.wikidata.org/wiki/Q773483","display_name":"Existential quantification","level":2,"score":0.25529998540878296},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.2533999979496002},{"id":"https://openalex.org/C3018023364","wikidata":"https://www.wikidata.org/wiki/Q425265","display_name":"Significant difference","level":2,"score":0.2362000048160553}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.10089","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.10089","pdf_url":"https://arxiv.org/pdf/2610.10089","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.2610.10089","doi":"https://doi.org/10.48550/arxiv.2610.10089","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.10089","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:2610.10089","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.10089","pdf_url":"https://arxiv.org/pdf/2610.10089","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/W7220991104.pdf","grobid_xml":"https://content.openalex.org/works/W7220991104.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7221753623","https://openalex.org/W1629488001","https://openalex.org/W2103357303","https://openalex.org/W1604774219","https://openalex.org/W2950494846","https://openalex.org/W2952559955","https://openalex.org/W4226023181","https://openalex.org/W3042988394","https://openalex.org/W1595846292","https://openalex.org/W1673961727"],"abstract_inverted_index":{"It":[0],"is":[1],"proved":[2],"that":[3,10],"there":[4],"exists":[5],"a":[6],"language":[7],"$L$":[8],"such":[9],"its":[11],"$\u03c9$-power":[12],"has":[13],"infinite":[14],"rank":[15],"in":[16],"the":[17,27],"difference":[18,29],"hierarchy":[19,30],"of":[20,31],"open":[21],"sets.":[22,33],"The":[23],"same":[24],"holds":[25],"for":[26],"decreasing":[28],"$\u03a0^0_2$":[32]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-10-09T00:00:00"}