{"id":"https://openalex.org/W7202212913","doi":"https://doi.org/10.48550/arxiv.2608.08426","title":"The elementary theory of full $n$-branching ordinal trees with successor functions","display_name":"The elementary theory of full $n$-branching ordinal trees with successor functions","publication_year":2026,"publication_date":"2026-08-09","ids":{"openalex":"https://openalex.org/W7202212913","doi":"https://doi.org/10.48550/arxiv.2608.08426"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.08426","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.08426","pdf_url":"https://arxiv.org/pdf/2608.08426","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":"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/2608.08426","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5146473141","display_name":"Junhong Chen","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chen, Junhong","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5146522201","display_name":"Yi Ru-Ya Zhang","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhang, Yi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"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":0.9965999722480774,"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":0.9965999722480774,"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":0.0010999999940395355,"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/T11567","display_name":"semigroups and automata theory","score":0.000699999975040555,"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/first-order-theories","display_name":"first-order theories","score":0.7039999961853027},{"id":"https://openalex.org/keywords/elementary-equivalence","display_name":"elementary equivalence","score":0.9330000281333923},{"id":"https://openalex.org/keywords/decidability","display_name":"decidability","score":0.9890000224113464},{"id":"https://openalex.org/keywords/successor-function","display_name":"successor function","score":0.5189999938011169}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9039999842643738},{"id":"https://openalex.org/C2776378722","wikidata":"https://www.wikidata.org/wiki/Q3454417","display_name":"Realizability","level":2,"score":0.7185999751091003},{"id":"https://openalex.org/C75306776","wikidata":"https://www.wikidata.org/wiki/Q7632662","display_name":"Successor cardinal","level":2,"score":0.6913999915122986},{"id":"https://openalex.org/C153269930","wikidata":"https://www.wikidata.org/wiki/Q430001","display_name":"Decidability","level":2,"score":0.6542999744415283},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5681999921798706},{"id":"https://openalex.org/C2778523021","wikidata":"https://www.wikidata.org/wiki/Q5532504","display_name":"Quantifier (linguistics)","level":2,"score":0.5224000215530396},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.41609999537467957},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.41600000858306885},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.38370001316070557},{"id":"https://openalex.org/C2778408900","wikidata":"https://www.wikidata.org/wiki/Q1329258","display_name":"Cardinal number (linguistics)","level":2,"score":0.3716000020503998},{"id":"https://openalex.org/C32278780","wikidata":"https://www.wikidata.org/wiki/Q1849020","display_name":"Quantifier elimination","level":2,"score":0.3653999865055084},{"id":"https://openalex.org/C47030870","wikidata":"https://www.wikidata.org/wiki/Q467606","display_name":"Model theory","level":2,"score":0.3612000048160553},{"id":"https://openalex.org/C25343380","wikidata":"https://www.wikidata.org/wiki/Q277521","display_name":"Relation (database)","level":2,"score":0.33809998631477356},{"id":"https://openalex.org/C204707403","wikidata":"https://www.wikidata.org/wiki/Q1152398","display_name":"Canonical form","level":2,"score":0.33059999346733093},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3124000132083893},{"id":"https://openalex.org/C2780102774","wikidata":"https://www.wikidata.org/wiki/Q4669873","display_name":"Absoluteness","level":2,"score":0.3100999891757965},{"id":"https://openalex.org/C203264685","wikidata":"https://www.wikidata.org/wiki/Q2328174","display_name":"Atomic formula","level":2,"score":0.29820001125335693},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.2858999967575073},{"id":"https://openalex.org/C2318724","wikidata":"https://www.wikidata.org/wiki/Q852732","display_name":"Proof theory","level":3,"score":0.258899986743927},{"id":"https://openalex.org/C138890893","wikidata":"https://www.wikidata.org/wiki/Q620006","display_name":"Order type","level":2,"score":0.2556999921798706}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.08426","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.08426","pdf_url":"https://arxiv.org/pdf/2608.08426","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2608.08426","doi":"https://doi.org/10.48550/arxiv.2608.08426","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.08426","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:2608.08426","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.08426","pdf_url":"https://arxiv.org/pdf/2608.08426","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":"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/W7202212913.pdf","grobid_xml":"https://content.openalex.org/works/W7202212913.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2790874222","https://openalex.org/W2138050599","https://openalex.org/W2257200480","https://openalex.org/W4360977267","https://openalex.org/W4234687429","https://openalex.org/W4319923644","https://openalex.org/W2105322061","https://openalex.org/W3170375357","https://openalex.org/W7214797228","https://openalex.org/W1989796321"],"abstract_inverted_index":{"We":[0,11,78],"investigate":[1],"the":[2,17,37,53,56,60,73,81,95],"first-order":[3,100],"theories":[4],"of":[5,16,31,52,63,75],"full":[6],"\\(n\\)-branching":[7],"ordinal":[8,38,65],"trees":[9,19,85],"\\(\\mathfrak{T}_\u03b1^n\\).":[10],"obtain":[12,68],"a":[13,69],"complete":[14],"classification":[15],"standard":[18,104],"up":[20],"to":[21,29],"elementary":[22],"equivalence:":[23],"every":[24],"\\(\\mathfrak{T}_\u03b1^n\\)":[25],"is":[26,98],"elementarily":[27],"equivalent":[28],"one":[30],"four":[32],"canonical":[33,42],"types":[34],"determined":[35],"by":[36],"\\(\u03b1\\).":[39],"For":[40],"each":[41],"type":[43],"we":[44,58],"establish":[45],"effective":[46],"quantifier":[47],"elimination":[48],"and":[49,67,86,92],"prove":[50],"decidability":[51],"theory.":[54],"Along":[55],"way":[57],"develop":[59],"realizability":[61],"theory":[62],"colored":[64],"characters":[66],"sharp":[70],"bound":[71],"on":[72],"length":[74],"minimal":[76],"witnesses.":[77],"also":[79],"clarify":[80],"relationship":[82],"between":[83],"these":[84],"monadic":[87],"second-order":[88],"logic":[89],"over":[90],"ordinals,":[91],"show":[93],"that":[94],"equal-height":[96],"relation":[97],"not":[99],"definable":[101],"in":[102],"any":[103],"tree.":[105]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-08-12T00:00:00"}