{"id":"https://openalex.org/W7222447448","doi":"https://doi.org/10.48550/arxiv.2610.22002","title":"Indiscernible Extraction in Theories with Bounded $k$-splitting","display_name":"Indiscernible Extraction in Theories with Bounded $k$-splitting","publication_year":2026,"publication_date":"2026-10-15","ids":{"openalex":"https://openalex.org/W7222447448","doi":"https://doi.org/10.48550/arxiv.2610.22002"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.22002","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.22002","pdf_url":"https://arxiv.org/pdf/2610.22002","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/2610.22002","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5124918541","display_name":"Connor Watson","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Watson, Connor","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5124918541"],"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":0.9990000128746033,"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":0.9990000128746033,"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":9.999999747378752e-05,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.0,"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/weakly-compact-cardinals","display_name":"weakly compact cardinals","score":0.8740000128746033},{"id":"https://openalex.org/keywords/model-theory","display_name":"model theory","score":0.46299999952316284},{"id":"https://openalex.org/keywords/zfc","display_name":"ZFC","score":0.6769999861717224}],"concepts":[{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.9135000109672546},{"id":"https://openalex.org/C40422974","wikidata":"https://www.wikidata.org/wiki/Q741248","display_name":"Assertion","level":2,"score":0.8180999755859375},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6481000185012817},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5830000042915344},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.37369999289512634},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3617999851703644},{"id":"https://openalex.org/C175454919","wikidata":"https://www.wikidata.org/wiki/Q2342396","display_name":"Bounded operator","level":3,"score":0.28189998865127563},{"id":"https://openalex.org/C4725764","wikidata":"https://www.wikidata.org/wiki/Q844704","display_name":"Extraction (chemistry)","level":2,"score":0.2732999920845032},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.24959999322891235},{"id":"https://openalex.org/C92928283","wikidata":"https://www.wikidata.org/wiki/Q4949981","display_name":"Bounded deformation","level":4,"score":0.23819999396800995}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.22002","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.22002","pdf_url":"https://arxiv.org/pdf/2610.22002","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.2610.22002","doi":"https://doi.org/10.48550/arxiv.2610.22002","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.22002","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.22002","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.22002","pdf_url":"https://arxiv.org/pdf/2610.22002","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/W7222447448.pdf","grobid_xml":"https://content.openalex.org/works/W7222447448.grobid-xml"},"referenced_works_count":4,"referenced_works":["https://openalex.org/W1998813503","https://openalex.org/W3208248642","https://openalex.org/W4396517301","https://openalex.org/W4414683288"],"related_works":["https://openalex.org/W4414683288","https://openalex.org/W2403214738","https://openalex.org/W7099578657","https://openalex.org/W4396517301","https://openalex.org/W1996512113","https://openalex.org/W3102546135","https://openalex.org/W2066285500","https://openalex.org/W7125254758","https://openalex.org/W7098409640","https://openalex.org/W3007855042"],"abstract_inverted_index":{"Hanson":[0],"introduced":[1],"the":[2,24,36,44],"class":[3],"of":[4,12,26,38,73],"theories":[5,22,64,80],"with":[6,81],"bounded":[7,75,82],"$k$-splitting,":[8],"a":[9,27,50],"higher-arity":[10],"notion":[11],"stability,":[13],"and":[14],"proved":[15],"an":[16],"indiscernible":[17,59],"extraction":[18,60],"result":[19],"for":[20,62],"those":[21],"assuming":[23],"existence":[25],"$k$-ineffable":[28],"cardinal.":[29],"In":[30],"this":[31],"article,":[32],"we":[33,68],"show":[34,69],"that":[35,47,70],"conclusion":[37],"Hanson's":[39,71],"theorem":[40],"is":[41],"equivalent":[42],"to":[43],"weaker":[45],"assertion":[46],"there":[48],"exists":[49],"weakly":[51],"compact":[52],"cardinal,":[53],"as":[54,56],"well":[55],"prove":[57],"additional":[58],"results":[61],"these":[63],"in":[65,79],"ZFC.":[66,86],"Finally,":[67],"construction":[72],"total":[74],"ultraimaginary":[76],"Morley":[77],"sequences":[78],"$k$-splitting":[83],"follows":[84],"from":[85]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-17T00:00:00"}
