{"id":"https://openalex.org/W2067714768","doi":"https://doi.org/10.1215/00294527-1731380","title":"The First-Order Syntax of Variadic Functions","display_name":"The First-Order Syntax of Variadic Functions","publication_year":2012,"publication_date":"2012-12-14","ids":{"openalex":"https://openalex.org/W2067714768","doi":"https://doi.org/10.1215/00294527-1731380","mag":"2067714768"},"language":"en","primary_location":{"id":"doi:10.1215/00294527-1731380","is_oa":true,"landing_page_url":"https://doi.org/10.1215/00294527-1731380","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-54/issue-1/The-First-Order-Syntax-of-Variadic-Functions/10.1215/00294527-1731380.pdf","source":{"id":"https://openalex.org/S78544662","display_name":"Notre Dame Journal of Formal Logic","issn_l":"0029-4527","issn":["0029-4527","1939-0726"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315698","host_organization_name":"Duke University Press","host_organization_lineage":["https://openalex.org/P4310315698","https://openalex.org/P4310315572"],"host_organization_lineage_names":["Duke University Press","Duke University"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Notre Dame Journal of Formal Logic","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-54/issue-1/The-First-Order-Syntax-of-Variadic-Functions/10.1215/00294527-1731380.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5016012515","display_name":"Samuel Allen Alexander","orcid":"https://orcid.org/0000-0002-7930-110X"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Samuel Alexander","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5016012515"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.11289976,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"54","issue":"1","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":0.968500018119812,"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":0.968500018119812,"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/T11567","display_name":"semigroups and automata theory","score":0.9395999908447266,"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/T12170","display_name":"History and Theory of Mathematics","score":0.907800018787384,"subfield":{"id":"https://openalex.org/subfields/2614","display_name":"Theoretical Computer Science"},"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/lemma","display_name":"Lemma (botany)","score":0.654910683631897},{"id":"https://openalex.org/keywords/syntax","display_name":"Syntax","score":0.6510392427444458},{"id":"https://openalex.org/keywords/substitution","display_name":"Substitution (logic)","score":0.6153749823570251},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6064902544021606},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5889507532119751},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5842630863189697},{"id":"https://openalex.org/keywords/quantifier-elimination","display_name":"Quantifier elimination","score":0.5455580949783325},{"id":"https://openalex.org/keywords/quantifier","display_name":"Quantifier (linguistics)","score":0.5331702828407288},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4734439551830292},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.45037898421287537},{"id":"https://openalex.org/keywords/abstract-syntax","display_name":"Abstract syntax","score":0.4500539302825928},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.39874935150146484},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3660717010498047},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.27615416049957275},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.1792784035205841},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.10655036568641663}],"concepts":[{"id":"https://openalex.org/C2777759810","wikidata":"https://www.wikidata.org/wiki/Q149316","display_name":"Lemma (botany)","level":3,"score":0.654910683631897},{"id":"https://openalex.org/C60048249","wikidata":"https://www.wikidata.org/wiki/Q37437","display_name":"Syntax","level":2,"score":0.6510392427444458},{"id":"https://openalex.org/C2778220771","wikidata":"https://www.wikidata.org/wiki/Q1522579","display_name":"Substitution (logic)","level":2,"score":0.6153749823570251},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6064902544021606},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5889507532119751},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5842630863189697},{"id":"https://openalex.org/C32278780","wikidata":"https://www.wikidata.org/wiki/Q1849020","display_name":"Quantifier elimination","level":2,"score":0.5455580949783325},{"id":"https://openalex.org/C2778523021","wikidata":"https://www.wikidata.org/wiki/Q5532504","display_name":"Quantifier (linguistics)","level":2,"score":0.5331702828407288},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4734439551830292},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.45037898421287537},{"id":"https://openalex.org/C114408938","wikidata":"https://www.wikidata.org/wiki/Q333373","display_name":"Abstract syntax","level":3,"score":0.4500539302825928},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.39874935150146484},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3660717010498047},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.27615416049957275},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.1792784035205841},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.10655036568641663},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C46757340","wikidata":"https://www.wikidata.org/wiki/Q43238","display_name":"Poaceae","level":2,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1215/00294527-1731380","is_oa":true,"landing_page_url":"https://doi.org/10.1215/00294527-1731380","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-54/issue-1/The-First-Order-Syntax-of-Variadic-Functions/10.1215/00294527-1731380.pdf","source":{"id":"https://openalex.org/S78544662","display_name":"Notre Dame Journal of Formal Logic","issn_l":"0029-4527","issn":["0029-4527","1939-0726"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315698","host_organization_name":"Duke University Press","host_organization_lineage":["https://openalex.org/P4310315698","https://openalex.org/P4310315572"],"host_organization_lineage_names":["Duke University Press","Duke University"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Notre Dame Journal of Formal Logic","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1105.4135","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1105.4135","pdf_url":"https://arxiv.org/pdf/1105.4135","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":"pmh:oai:CULeuclid:euclid.ndjfl/1355494522","is_oa":false,"landing_page_url":"https://projecteuclid.org/euclid.ndjfl/1355494522","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"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":"","raw_type":"Text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.765.5022","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.765.5022","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/1105.4135.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1215/00294527-1731380","is_oa":true,"landing_page_url":"https://doi.org/10.1215/00294527-1731380","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-54/issue-1/The-First-Order-Syntax-of-Variadic-Functions/10.1215/00294527-1731380.pdf","source":{"id":"https://openalex.org/S78544662","display_name":"Notre Dame Journal of Formal Logic","issn_l":"0029-4527","issn":["0029-4527","1939-0726"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315698","host_organization_name":"Duke University Press","host_organization_lineage":["https://openalex.org/P4310315698","https://openalex.org/P4310315572"],"host_organization_lineage_names":["Duke University Press","Duke University"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Notre Dame Journal of Formal Logic","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2067714768.pdf","grobid_xml":"https://content.openalex.org/works/W2067714768.grobid-xml"},"referenced_works_count":10,"referenced_works":["https://openalex.org/W270257982","https://openalex.org/W1492568604","https://openalex.org/W1605752106","https://openalex.org/W2042181181","https://openalex.org/W2081739832","https://openalex.org/W2121105821","https://openalex.org/W2121898499","https://openalex.org/W2181475448","https://openalex.org/W2324843770","https://openalex.org/W3099960354"],"related_works":["https://openalex.org/W4214737172","https://openalex.org/W3012938552","https://openalex.org/W2324712051","https://openalex.org/W2798639752","https://openalex.org/W4287825236","https://openalex.org/W1524103539","https://openalex.org/W1239946963","https://openalex.org/W1973527399","https://openalex.org/W71729059","https://openalex.org/W2068866297"],"abstract_inverted_index":{"We":[0],"extend":[1],"first-order":[2],"logic":[3],"to":[4,19,25],"include":[5],"variadic":[6],"function":[7],"symbols":[8],"and":[9,23],"prove":[10],"a":[11],"substitution":[12],"lemma.":[13],"Two":[14],"applications":[15],"are":[16],"given:":[17],"one":[18,24],"bounded":[20],"quantifier":[21],"elimination":[22],"the":[26],"definability":[27],"of":[28],"certain":[29],"Borel":[30],"sets.":[31]},"counts_by_year":[],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
