{"id":"https://openalex.org/W2139026098","doi":"https://doi.org/10.2307/2275172","title":"Arithmetic definability by formulas with two quantifiers","display_name":"Arithmetic definability by formulas with two quantifiers","publication_year":1992,"publication_date":"1992-03-01","ids":{"openalex":"https://openalex.org/W2139026098","doi":"https://doi.org/10.2307/2275172","mag":"2139026098"},"language":"en","primary_location":{"id":"doi:10.2307/2275172","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2275172","pdf_url":null,"source":{"id":"https://openalex.org/S177675236","display_name":"Journal of Symbolic Logic","issn_l":"0022-4812","issn":["0022-4812","1943-5886"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Symbolic Logic","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5110127269","display_name":"Shih Ping Tung","orcid":null},"institutions":[{"id":"https://openalex.org/I151221077","display_name":"Chung Yuan Christian University","ror":"https://ror.org/02w8ws377","country_code":"TW","type":"education","lineage":["https://openalex.org/I151221077"]}],"countries":["TW"],"is_corresponding":true,"raw_author_name":"Shih Ping Tung","raw_affiliation_strings":["Department of Mathematics, Chung Yuan Christian University, Chung Li, Taiwan 32023, Republic of China","Department of Mathematics, Chung-Yuan Christian University, Chung-Li, Taiwan 32023, Republic of China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Chung Yuan Christian University, Chung Li, Taiwan 32023, Republic of China","institution_ids":["https://openalex.org/I151221077"]},{"raw_affiliation_string":"Department of Mathematics, Chung-Yuan Christian University, Chung-Li, Taiwan 32023, Republic of China","institution_ids":["https://openalex.org/I151221077"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5110127269"],"corresponding_institution_ids":["https://openalex.org/I151221077"],"apc_list":null,"apc_paid":null,"fwci":1.0211,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.77245636,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"57","issue":"1","first_page":"1","last_page":"11"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.989799976348877,"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":0.989799976348877,"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/T13400","display_name":"Mathematical and Theoretical Analysis","score":0.967199981212616,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9580000042915344,"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/quantifier-elimination","display_name":"Quantifier elimination","score":0.8313074707984924},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7721067070960999},{"id":"https://openalex.org/keywords/quantifier","display_name":"Quantifier (linguistics)","score":0.7003190517425537},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.6406185030937195},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5743485689163208},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.5443522334098816},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.49931979179382324},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.44284284114837646},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.43461453914642334},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.26942211389541626},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1324842870235443},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.05198782682418823},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.051189929246902466}],"concepts":[{"id":"https://openalex.org/C32278780","wikidata":"https://www.wikidata.org/wiki/Q1849020","display_name":"Quantifier elimination","level":2,"score":0.8313074707984924},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7721067070960999},{"id":"https://openalex.org/C2778523021","wikidata":"https://www.wikidata.org/wiki/Q5532504","display_name":"Quantifier (linguistics)","level":2,"score":0.7003190517425537},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.6406185030937195},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5743485689163208},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.5443522334098816},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.49931979179382324},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.44284284114837646},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.43461453914642334},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.26942211389541626},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1324842870235443},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.05198782682418823},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.051189929246902466},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.2307/2275172","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2275172","pdf_url":null,"source":{"id":"https://openalex.org/S177675236","display_name":"Journal of Symbolic Logic","issn_l":"0022-4812","issn":["0022-4812","1943-5886"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Symbolic Logic","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.jsl/1183743887","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1183743887","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"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/8","score":0.5699999928474426,"display_name":"Decent work and economic growth"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":6,"referenced_works":["https://openalex.org/W1558611215","https://openalex.org/W1732310309","https://openalex.org/W2011938854","https://openalex.org/W2047249455","https://openalex.org/W2135556826","https://openalex.org/W2151085125"],"related_works":["https://openalex.org/W4214737172","https://openalex.org/W3012938552","https://openalex.org/W2170779139","https://openalex.org/W2324712051","https://openalex.org/W4287825236","https://openalex.org/W1239946963","https://openalex.org/W71729059","https://openalex.org/W1524103539","https://openalex.org/W1973527399","https://openalex.org/W2798639752"],"abstract_inverted_index":{"Abstract":[0],"We":[1],"give":[2],"necessary":[3,32],"conditions":[4,33],"for":[5],"a":[6,12,15,47,54],"set":[7],"to":[8],"be":[9],"definable":[10,44],"by":[11,45],"formula":[13,48],"with":[14],"universal":[16],"quantifier":[17,21],"and":[18],"an":[19],"existential":[20],"over":[22,49],"algebraic":[23,27],"integer":[24],"rings":[25],"or":[26],"number":[28],"fields.":[29],"From":[30],"these":[31],"we":[34],"obtain":[35],"some":[36],"undefinability":[37],"results.":[38],"For":[39],"example,":[40],"N":[41],"is":[42],"not":[43],"such":[46],"Z":[50],".":[51],"This":[52],"extends":[53],"previous":[55],"result":[56],"of":[57],"R.":[58],"M.":[59],"Robinson.":[60]},"counts_by_year":[],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}