{"id":"https://openalex.org/W2028626203","doi":"https://doi.org/10.2178/jsl/1190150100","title":"An isomorphism between monoids of external embeddings: About definability in arithmetic","display_name":"An isomorphism between monoids of external embeddings: About definability in arithmetic","publication_year":2002,"publication_date":"2002-06-01","ids":{"openalex":"https://openalex.org/W2028626203","doi":"https://doi.org/10.2178/jsl/1190150100","mag":"2028626203"},"language":"en","primary_location":{"id":"doi:10.2178/jsl/1190150100","is_oa":false,"landing_page_url":"https://doi.org/10.2178/jsl/1190150100","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/A5044551951","display_name":"Mihai Prunescu","orcid":"https://orcid.org/0000-0003-1627-050X"},"institutions":[{"id":"https://openalex.org/I36522303","display_name":"Universit\u00e4t Greifswald","ror":"https://ror.org/00r1edq15","country_code":"DE","type":"education","lineage":["https://openalex.org/I36522303"]},{"id":"https://openalex.org/I58077936","display_name":"Romanian Academy","ror":"https://ror.org/0561n6946","country_code":"RO","type":"archive","lineage":["https://openalex.org/I58077936"]},{"id":"https://openalex.org/I33800924","display_name":"Academy of Romanian Scientists","ror":"https://ror.org/04ybnj478","country_code":"RO","type":"facility","lineage":["https://openalex.org/I33800924"]}],"countries":["DE","RO"],"is_corresponding":true,"raw_author_name":"Mihai Prunescu","raw_affiliation_strings":["Institut F\u00fcr Mathematik und Informatik, Universit\u00e4t Greifswald, Germany","Institute of Mathematics of the Romanian Academy, Bucharest, Romania, E-mail:"],"affiliations":[{"raw_affiliation_string":"Institut F\u00fcr Mathematik und Informatik, Universit\u00e4t Greifswald, Germany","institution_ids":["https://openalex.org/I36522303"]},{"raw_affiliation_string":"Institute of Mathematics of the Romanian Academy, Bucharest, Romania, E-mail:","institution_ids":["https://openalex.org/I58077936","https://openalex.org/I33800924"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5044551951"],"corresponding_institution_ids":["https://openalex.org/I33800924","https://openalex.org/I36522303","https://openalex.org/I58077936"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.13049826,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"67","issue":"2","first_page":"598","last_page":"620"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9839000105857849,"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"}},"topics":[{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9839000105857849,"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":0.9646999835968018,"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/T13400","display_name":"Mathematical and Theoretical Analysis","score":0.9621000289916992,"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/isomorphism","display_name":"Isomorphism (crystallography)","score":0.8031786680221558},{"id":"https://openalex.org/keywords/statement","display_name":"Statement (logic)","score":0.6640973091125488},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.635258674621582},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.564896285533905},{"id":"https://openalex.org/keywords/second-order-arithmetic","display_name":"Second-order arithmetic","score":0.5596388578414917},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.5038647055625916},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.45932647585868835},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.40870606899261475},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.33412444591522217},{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.06252855062484741},{"id":"https://openalex.org/keywords/linguistics","display_name":"Linguistics","score":0.04819628596305847},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.03737384080886841}],"concepts":[{"id":"https://openalex.org/C203436722","wikidata":"https://www.wikidata.org/wiki/Q902950","display_name":"Isomorphism (crystallography)","level":3,"score":0.8031786680221558},{"id":"https://openalex.org/C2777026412","wikidata":"https://www.wikidata.org/wiki/Q2684591","display_name":"Statement (logic)","level":2,"score":0.6640973091125488},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.635258674621582},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.564896285533905},{"id":"https://openalex.org/C65148605","wikidata":"https://www.wikidata.org/wiki/Q7442973","display_name":"Second-order arithmetic","level":3,"score":0.5596388578414917},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.5038647055625916},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.45932647585868835},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.40870606899261475},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.33412444591522217},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.06252855062484741},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.04819628596305847},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.03737384080886841},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C8010536","wikidata":"https://www.wikidata.org/wiki/Q160398","display_name":"Crystallography","level":1,"score":0.0},{"id":"https://openalex.org/C115624301","wikidata":"https://www.wikidata.org/wiki/Q895901","display_name":"Crystal structure","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/C97489613","wikidata":"https://www.wikidata.org/wiki/Q842755","display_name":"Peano axioms","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.2178/jsl/1190150100","is_oa":false,"landing_page_url":"https://doi.org/10.2178/jsl/1190150100","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/1190150100","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1190150100","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:10.1.1.666.3471","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.666.3471","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://home.mathematik.uni-freiburg.de/prunescu/isomorph.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":33,"referenced_works":["https://openalex.org/W148161311","https://openalex.org/W1511020764","https://openalex.org/W1521659972","https://openalex.org/W1600946210","https://openalex.org/W1601654835","https://openalex.org/W1965535978","https://openalex.org/W1978114483","https://openalex.org/W1983097969","https://openalex.org/W1994747442","https://openalex.org/W1998146115","https://openalex.org/W2011938854","https://openalex.org/W2026914071","https://openalex.org/W2059568104","https://openalex.org/W2063770561","https://openalex.org/W2080000094","https://openalex.org/W2082737502","https://openalex.org/W2107308446","https://openalex.org/W2157736452","https://openalex.org/W2183676805","https://openalex.org/W2300684981","https://openalex.org/W2331987008","https://openalex.org/W2573016414","https://openalex.org/W2971268466","https://openalex.org/W2977904728","https://openalex.org/W3130727218","https://openalex.org/W4231639377","https://openalex.org/W4233607861","https://openalex.org/W4238505766","https://openalex.org/W4245511791","https://openalex.org/W4248480617","https://openalex.org/W4256369010","https://openalex.org/W6644583786","https://openalex.org/W6649330678"],"related_works":["https://openalex.org/W2083774956","https://openalex.org/W2181927644","https://openalex.org/W2158464203","https://openalex.org/W1577151476","https://openalex.org/W1944601446","https://openalex.org/W4247547172","https://openalex.org/W4249530125","https://openalex.org/W2078971842","https://openalex.org/W2756505297","https://openalex.org/W3196847358"],"abstract_inverted_index":{"Abstract":[0],"We":[1,28],"use":[2],"a":[3],"new":[4],"version":[5],"of":[6,10,18],"the":[7],"Definability":[8],"Theorem":[9],"Beth":[11],"in":[12,24],"order":[13],"to":[14],"unify":[15],"classical":[16],"theorems":[17],"Yuri":[19],"Matiyasevich":[20],"and":[21,39],"Jan":[22],"Denef":[23],"one":[25],"structural":[26],"statement.":[27],"give":[29],"similar":[30],"forms":[31],"for":[32],"other":[33],"important":[34],"definability":[35],"results":[36],"from":[37],"Arithmetic":[38],"Number":[40],"Theory.":[41]},"counts_by_year":[],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}