{"id":"https://openalex.org/W3037431022","doi":"https://doi.org/10.2178/bsl/1305810912","title":"Defining Integers","display_name":"Defining Integers","publication_year":2011,"publication_date":"2011-05-19","ids":{"openalex":"https://openalex.org/W3037431022","doi":"https://doi.org/10.2178/bsl/1305810912","mag":"3037431022"},"language":"en","primary_location":{"id":"doi:10.2178/bsl/1305810912","is_oa":true,"landing_page_url":"https://doi.org/10.2178/bsl/1305810912","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/79E08945B4C30E9F67D7FDF2329422D8/S1079898600000548a.pdf/div-class-title-defining-integers-div.pdf","source":{"id":"https://openalex.org/S130801046","display_name":"Bulletin of Symbolic Logic","issn_l":"1079-8986","issn":["1079-8986","1943-5894"],"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":"The Bulletin of Symbolic Logic","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/79E08945B4C30E9F67D7FDF2329422D8/S1079898600000548a.pdf/div-class-title-defining-integers-div.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5020820702","display_name":"Alexandra Shlapentokh","orcid":"https://orcid.org/0000-0003-1990-909X"},"institutions":[{"id":"https://openalex.org/I186335123","display_name":"East Carolina University","ror":"https://ror.org/01vx35703","country_code":"US","type":"education","lineage":["https://openalex.org/I186335123"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Alexandra Shlapentokh","raw_affiliation_strings":["Department of Mathematics, East Carolina University, Greenville, NC 27858, USAE-mail:"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, East Carolina University, Greenville, NC 27858, USAE-mail:","institution_ids":["https://openalex.org/I186335123"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5020820702"],"corresponding_institution_ids":["https://openalex.org/I186335123"],"apc_list":null,"apc_paid":null,"fwci":0.7523,"has_fulltext":true,"cited_by_count":8,"citation_normalized_percentile":{"value":0.73922776,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"17","issue":"2","first_page":"230","last_page":"251"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number 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/T10061","display_name":"Algebraic Geometry and Number 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/T12170","display_name":"History and Theory of Mathematics","score":0.9984999895095825,"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"}},{"id":"https://openalex.org/T11166","display_name":"Analytic Number Theory Research","score":0.9983999729156494,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4962347149848938},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.48910409212112427},{"id":"https://openalex.org/keywords/algebraic-number-field","display_name":"Algebraic number field","score":0.45567166805267334},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.37902480363845825},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.33643239736557007},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.3317651152610779},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.22222688794136047}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4962347149848938},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.48910409212112427},{"id":"https://openalex.org/C12657307","wikidata":"https://www.wikidata.org/wiki/Q616608","display_name":"Algebraic number field","level":2,"score":0.45567166805267334},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.37902480363845825},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.33643239736557007},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.3317651152610779},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.22222688794136047}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.2178/bsl/1305810912","is_oa":true,"landing_page_url":"https://doi.org/10.2178/bsl/1305810912","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/79E08945B4C30E9F67D7FDF2329422D8/S1079898600000548a.pdf/div-class-title-defining-integers-div.pdf","source":{"id":"https://openalex.org/S130801046","display_name":"Bulletin of Symbolic Logic","issn_l":"1079-8986","issn":["1079-8986","1943-5894"],"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":"The Bulletin of Symbolic Logic","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.bsl/1305810912","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.bsl/1305810912","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":{"id":"doi:10.2178/bsl/1305810912","is_oa":true,"landing_page_url":"https://doi.org/10.2178/bsl/1305810912","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/79E08945B4C30E9F67D7FDF2329422D8/S1079898600000548a.pdf/div-class-title-defining-integers-div.pdf","source":{"id":"https://openalex.org/S130801046","display_name":"Bulletin of Symbolic Logic","issn_l":"1079-8986","issn":["1079-8986","1943-5894"],"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":"The Bulletin of Symbolic Logic","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G8386690539","display_name":"Definability and Decidability over Algebraic Extensions of Product Formula Fields","funder_award_id":"0650927","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320306193","display_name":"John Templeton Foundation","ror":"https://ror.org/035tnyy05"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3037431022.pdf","grobid_xml":"https://content.openalex.org/works/W3037431022.grobid-xml"},"referenced_works_count":41,"referenced_works":["https://openalex.org/W645693063","https://openalex.org/W1486898453","https://openalex.org/W1523983089","https://openalex.org/W1558576569","https://openalex.org/W1575996225","https://openalex.org/W1619977925","https://openalex.org/W1650941180","https://openalex.org/W1651628549","https://openalex.org/W1719758153","https://openalex.org/W1978114483","https://openalex.org/W1987450159","https://openalex.org/W1992184757","https://openalex.org/W1994747442","https://openalex.org/W2004193076","https://openalex.org/W2009370726","https://openalex.org/W2011938854","https://openalex.org/W2015376829","https://openalex.org/W2034310947","https://openalex.org/W2049262732","https://openalex.org/W2058177358","https://openalex.org/W2076040392","https://openalex.org/W2078890952","https://openalex.org/W2080000094","https://openalex.org/W2085881424","https://openalex.org/W2087721808","https://openalex.org/W2107519895","https://openalex.org/W2126495200","https://openalex.org/W2530006810","https://openalex.org/W2905135108","https://openalex.org/W2952547600","https://openalex.org/W3105629360","https://openalex.org/W4233607861","https://openalex.org/W4234648161","https://openalex.org/W4238357211","https://openalex.org/W4238505766","https://openalex.org/W4247052524","https://openalex.org/W4248995378","https://openalex.org/W4254784218","https://openalex.org/W4255344569","https://openalex.org/W6649330678","https://openalex.org/W6764473497"],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2042127053","https://openalex.org/W1987894575","https://openalex.org/W2085020044","https://openalex.org/W2329457535"],"abstract_inverted_index":{"Abstract":[0],"This":[1],"paper":[2],"surveys":[3],"the":[4,8,24,30,44,48,56],"recent":[5],"developments":[6],"in":[7,61],"area":[9],"that":[10],"grew":[11],"out":[12],"of":[13,19,26,32,34,53,58,63],"attempts":[14],"to":[15],"solve":[16],"an":[17],"analog":[18],"Hilbert's":[20],"Tenth":[21],"Problem":[22],"for":[23],"field":[25],"rational":[27],"numbers":[28],"and":[29],"rings":[31],"integers":[33],"number":[35],"fields.":[36],"It":[37],"is":[38],"based":[39],"on":[40],"a":[41],"plenary":[42],"talk":[43],"author":[45],"gave":[46],"at":[47,55],"annual":[49],"North":[50],"American":[51],"meeting":[52],"ASL":[54],"University":[57],"Notre":[59],"Dame":[60],"May":[62],"2009.":[64]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2020-07-02T00:00:00"}
