{"id":"https://openalex.org/W2080999509","doi":"https://doi.org/10.2178/jsl/1278682210","title":"On complex exponentiation restricted to the integers","display_name":"On complex exponentiation restricted to the integers","publication_year":2010,"publication_date":"2010-07-09","ids":{"openalex":"https://openalex.org/W2080999509","doi":"https://doi.org/10.2178/jsl/1278682210","mag":"2080999509"},"language":"en","primary_location":{"id":"doi:10.2178/jsl/1278682210","is_oa":false,"landing_page_url":"https://doi.org/10.2178/jsl/1278682210","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":"The 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/A5011521416","display_name":"Carlo Toffalori","orcid":"https://orcid.org/0000-0002-5570-8597"},"institutions":[{"id":"https://openalex.org/I112859197","display_name":"Universit\u00e0 di Camerino","ror":"https://ror.org/0005w8d69","country_code":"IT","type":"education","lineage":["https://openalex.org/I112859197"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Carlo Toffalori","raw_affiliation_strings":["Department of Mathematics and Computer Science, University of Camerino, Via Madonna Delle Carceri 9, 62032 Camerino, Italy. E-mail:","Department of Mathematics and Computer Science, University of Camerino, Via Madonna Delle Carceri 9, 62032 Camerino, Italy. E-mail: carlo.toffalori@unicam.it"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science, University of Camerino, Via Madonna Delle Carceri 9, 62032 Camerino, Italy. E-mail:","institution_ids":["https://openalex.org/I112859197"]},{"raw_affiliation_string":"Department of Mathematics and Computer Science, University of Camerino, Via Madonna Delle Carceri 9, 62032 Camerino, Italy. E-mail: carlo.toffalori@unicam.it","institution_ids":["https://openalex.org/I112859197"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5065433052","display_name":"Kathryn Vozoris","orcid":null},"institutions":[{"id":"https://openalex.org/I112859197","display_name":"Universit\u00e0 di Camerino","ror":"https://ror.org/0005w8d69","country_code":"IT","type":"education","lineage":["https://openalex.org/I112859197"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Kathryn Vozoris","raw_affiliation_strings":["Department of Mathematics and Computer Science, University of Camerino, Via Madonna Delle Carceri 9, 62032 Camerino, Italy. E-mail:","Department of Mathematics and Computer Science, University of Camerino, Via Madonna Delle Carceri 9, 62032 Camerino, Italy. E-mail: kathryn.vozoris@unicam.it"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science, University of Camerino, Via Madonna Delle Carceri 9, 62032 Camerino, Italy. E-mail:","institution_ids":["https://openalex.org/I112859197"]},{"raw_affiliation_string":"Department of Mathematics and Computer Science, University of Camerino, Via Madonna Delle Carceri 9, 62032 Camerino, Italy. E-mail: kathryn.vozoris@unicam.it","institution_ids":["https://openalex.org/I112859197"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I112859197"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.14303264,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"75","issue":"3","first_page":"955","last_page":"970"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9987000226974487,"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":0.9987000226974487,"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":0.9919000267982483,"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/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.9805999994277954,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/exponentiation","display_name":"Exponentiation","score":0.8698086738586426},{"id":"https://openalex.org/keywords/subring","display_name":"Subring","score":0.8304480314254761},{"id":"https://openalex.org/keywords/modulo","display_name":"Modulo","score":0.7877861261367798},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6421090364456177},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5314670205116272},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.5281016230583191},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.4861688017845154},{"id":"https://openalex.org/keywords/ring-of-integers","display_name":"Ring of integers","score":0.4365542531013489},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3892773985862732},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.370685338973999},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.3434554934501648},{"id":"https://openalex.org/keywords/algebraic-number-field","display_name":"Algebraic number field","score":0.2998034358024597},{"id":"https://openalex.org/keywords/ring","display_name":"Ring (chemistry)","score":0.15817424654960632},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.10759371519088745}],"concepts":[{"id":"https://openalex.org/C81539297","wikidata":"https://www.wikidata.org/wiki/Q33456","display_name":"Exponentiation","level":2,"score":0.8698086738586426},{"id":"https://openalex.org/C21714298","wikidata":"https://www.wikidata.org/wiki/Q929536","display_name":"Subring","level":3,"score":0.8304480314254761},{"id":"https://openalex.org/C54732982","wikidata":"https://www.wikidata.org/wiki/Q1415345","display_name":"Modulo","level":2,"score":0.7877861261367798},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6421090364456177},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5314670205116272},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.5281016230583191},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.4861688017845154},{"id":"https://openalex.org/C164810661","wikidata":"https://www.wikidata.org/wiki/Q1358313","display_name":"Ring of integers","level":3,"score":0.4365542531013489},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3892773985862732},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.370685338973999},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.3434554934501648},{"id":"https://openalex.org/C12657307","wikidata":"https://www.wikidata.org/wiki/Q616608","display_name":"Algebraic number field","level":2,"score":0.2998034358024597},{"id":"https://openalex.org/C2780378348","wikidata":"https://www.wikidata.org/wiki/Q25351438","display_name":"Ring (chemistry)","level":2,"score":0.15817424654960632},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.10759371519088745},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.2178/jsl/1278682210","is_oa":false,"landing_page_url":"https://doi.org/10.2178/jsl/1278682210","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":"The Journal of Symbolic Logic","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.jsl/1278682210","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1278682210","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:pubblicazioni.unicam.it:11581/202799","is_oa":false,"landing_page_url":"http://hdl.handle.net/11581/202799","pdf_url":null,"source":{"id":"https://openalex.org/S4306400819","display_name":"Unicam Scientific Publications (University of Camerino)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I112859197","host_organization_name":"Universit\u00e0 di Camerino","host_organization_lineage":["https://openalex.org/I112859197"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":7,"referenced_works":["https://openalex.org/W1556189547","https://openalex.org/W1822440022","https://openalex.org/W1976209905","https://openalex.org/W2014230531","https://openalex.org/W2129678180","https://openalex.org/W2223917138","https://openalex.org/W2308676214"],"related_works":["https://openalex.org/W2532989613","https://openalex.org/W1634118047","https://openalex.org/W2122450783","https://openalex.org/W4301409452","https://openalex.org/W2065772962","https://openalex.org/W3021217617","https://openalex.org/W2085491127","https://openalex.org/W2021409800","https://openalex.org/W4327812131","https://openalex.org/W1966445873"],"abstract_inverted_index":{"Abstract":[0],"We":[1],"provide":[2],"a":[3],"first":[4,26],"order":[5,27],"axiomatization":[6],"of":[7,10,22,29],"the":[8,11,15,20,25],"expansion":[9],"complex":[12],"field":[13],"by":[14],"exponential":[16],"function":[17],"restricted":[18],"to":[19],"subring":[21],"integers":[23],"modulo":[24],"theory":[28],"(Z,":[30],"+,":[31],"\u2212).":[32]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
