{"id":"https://openalex.org/W2036224946","doi":"https://doi.org/10.2307/2275227","title":"Decidability and undecidability of theories with a predicate for the primes","display_name":"Decidability and undecidability of theories with a predicate for the primes","publication_year":1993,"publication_date":"1993-06-01","ids":{"openalex":"https://openalex.org/W2036224946","doi":"https://doi.org/10.2307/2275227","mag":"2036224946"},"language":"en","primary_location":{"id":"doi:10.2307/2275227","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2275227","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/A5103508411","display_name":"Paul T. Bateman","orcid":null},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"P. T. Bateman","raw_affiliation_strings":["Department of Mathematics, University of Illinois, Urbana, Illinois61801, E-mail:","#N#\u2004University of Illinois"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Illinois, Urbana, Illinois61801, E-mail:","institution_ids":["https://openalex.org/I157725225"]},{"raw_affiliation_string":"#N#\u2004University of Illinois","institution_ids":["https://openalex.org/I157725225"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5015653981","display_name":"C. G. Jockusch","orcid":null},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"C. G. Jockusch","raw_affiliation_strings":["Department of Mathematics, University of Illinois, Urbana, Illinois61801, E-mail:","#N#\u2004University of Illinois"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Illinois, Urbana, Illinois61801, E-mail:","institution_ids":["https://openalex.org/I157725225"]},{"raw_affiliation_string":"#N#\u2004University of Illinois","institution_ids":["https://openalex.org/I157725225"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5080340008","display_name":"Alan R. Woods","orcid":null},"institutions":[{"id":"https://openalex.org/I177877127","display_name":"University of Western Australia","ror":"https://ror.org/047272k79","country_code":"AU","type":"education","lineage":["https://openalex.org/I177877127"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"A. R. Woods","raw_affiliation_strings":["Department of Mathematics, University of Western Australia, Nedlands, Western Australia 6009, Australia, E-mail:","School of Mathematics and Statistics"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Western Australia, Nedlands, Western Australia 6009, Australia, E-mail:","institution_ids":["https://openalex.org/I177877127"]},{"raw_affiliation_string":"School of Mathematics and Statistics","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5103508411"],"corresponding_institution_ids":["https://openalex.org/I157725225"],"apc_list":null,"apc_paid":null,"fwci":0.5212,"has_fulltext":false,"cited_by_count":21,"citation_normalized_percentile":{"value":0.64200585,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"58","issue":"2","first_page":"672","last_page":"687"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9954000115394592,"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":0.9954000115394592,"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/T11567","display_name":"semigroups and automata theory","score":0.9886999726295471,"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/T10126","display_name":"Logic, programming, and type systems","score":0.9434999823570251,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/decidability","display_name":"Decidability","score":0.8738812208175659},{"id":"https://openalex.org/keywords/undecidable-problem","display_name":"Undecidable problem","score":0.864773154258728},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7855232954025269},{"id":"https://openalex.org/keywords/predicate","display_name":"Predicate (mathematical logic)","score":0.6097198128700256},{"id":"https://openalex.org/keywords/successor-cardinal","display_name":"Successor cardinal","score":0.5717467665672302},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5587639212608337},{"id":"https://openalex.org/keywords/monadic-predicate-calculus","display_name":"Monadic predicate calculus","score":0.5044296979904175},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.41735103726387024},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3890214264392853},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.11500599980354309},{"id":"https://openalex.org/keywords/higher-order-logic","display_name":"Higher-order logic","score":0.06726855039596558}],"concepts":[{"id":"https://openalex.org/C153269930","wikidata":"https://www.wikidata.org/wiki/Q430001","display_name":"Decidability","level":2,"score":0.8738812208175659},{"id":"https://openalex.org/C192034797","wikidata":"https://www.wikidata.org/wiki/Q3502995","display_name":"Undecidable problem","level":3,"score":0.864773154258728},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7855232954025269},{"id":"https://openalex.org/C140146324","wikidata":"https://www.wikidata.org/wiki/Q1144319","display_name":"Predicate (mathematical logic)","level":2,"score":0.6097198128700256},{"id":"https://openalex.org/C75306776","wikidata":"https://www.wikidata.org/wiki/Q7632662","display_name":"Successor cardinal","level":2,"score":0.5717467665672302},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5587639212608337},{"id":"https://openalex.org/C124656256","wikidata":"https://www.wikidata.org/wiki/Q6897882","display_name":"Monadic predicate calculus","level":4,"score":0.5044296979904175},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.41735103726387024},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3890214264392853},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.11500599980354309},{"id":"https://openalex.org/C169896238","wikidata":"https://www.wikidata.org/wiki/Q1644136","display_name":"Higher-order logic","level":3,"score":0.06726855039596558},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"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/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C102993220","wikidata":"https://www.wikidata.org/wiki/Q387196","display_name":"Description logic","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.2307/2275227","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2275227","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:pure.atira.dk:publications/b879d67b-1af1-4445-a764-e0977301f6b6","is_oa":false,"landing_page_url":"https://research-repository.uwa.edu.au/en/publications/b879d67b-1af1-4445-a764-e0977301f6b6","pdf_url":null,"source":{"id":"https://openalex.org/S4306402523","display_name":"UWA Profiles and Research Repository (University of Western Australia)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I177877127","host_organization_name":"The University of Western Australia","host_organization_lineage":["https://openalex.org/I177877127"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Bateman , P T , Jockusch , C G & Woods , A 1993 , ' Decidability and undecidability of theories with a predicate for the primes. ' , Journal of Symbolic Logic , vol. 58 , pp. 672-687 . https://doi.org/10.2307/2275227","raw_type":"article"},{"id":"pmh:oai:CULeuclid:euclid.jsl/1183744255","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1183744255","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":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W820979427","https://openalex.org/W1487855130","https://openalex.org/W1520256591","https://openalex.org/W1584078376","https://openalex.org/W1970999740","https://openalex.org/W1976772375","https://openalex.org/W1983682288","https://openalex.org/W1985871005","https://openalex.org/W2002089154","https://openalex.org/W2007981995","https://openalex.org/W2021891065","https://openalex.org/W2022485134","https://openalex.org/W2026134631","https://openalex.org/W2047860586","https://openalex.org/W2055692640","https://openalex.org/W2062403215","https://openalex.org/W2072057555","https://openalex.org/W2085311468","https://openalex.org/W2094912129","https://openalex.org/W2131742729","https://openalex.org/W2162583406","https://openalex.org/W2166279524","https://openalex.org/W3128307576","https://openalex.org/W4205178514","https://openalex.org/W4231685078","https://openalex.org/W4240244556","https://openalex.org/W4302339081","https://openalex.org/W6641740895"],"related_works":["https://openalex.org/W2972379433","https://openalex.org/W1501430220","https://openalex.org/W2989332944","https://openalex.org/W2021891065","https://openalex.org/W2583549044","https://openalex.org/W2119045600","https://openalex.org/W2584984136","https://openalex.org/W1542027783","https://openalex.org/W129916058","https://openalex.org/W1998665045"],"abstract_inverted_index":{"Abstract":[0],"It":[1],"is":[2,24,29,39,50,67,71,78,99],"shown,":[3,51],"assuming":[4],"the":[5,12,16,25,46,53,57,72],"linear":[6],"case":[7],"of":[8,15,27,36,61,84,90,96],"Schinzel's":[9],"Hypothesis,":[10],"that":[11,34,56],"first-order":[13,40],"theory":[14,60],"structure":[17],"\u3008\u03c9;":[18],"+,":[19],"P":[20,23,65],"\u3009,":[21],"where":[22,69],"set":[26],"primes,":[28],"undecidable":[30],"and,":[31],"in":[32,42],"fact,":[33],"multiplication":[35],"natural":[37],"numbers":[38],"definable":[41],"this":[43],"structure.":[44],"In":[45],"other":[47],"direction,":[48],"it":[49],"from":[52],"same":[54],"hypothesis,":[55],"monadic":[58,91],"second-order":[59],"\u3008\u03c9":[62],"S":[63,70],",":[64],"\u3009":[66],"decidable,":[68],"successor":[73],"function.":[74],"The":[75],"latter":[76],"result":[77,83,98],"proved":[79],"using":[80],"a":[81,94],"general":[82],"A.":[85],"L.":[86],"Sem\u00ebnov":[87],"on":[88],"decidability":[89],"theories,":[92],"and":[93],"proof":[95],"Sem\u00ebnov's":[97],"presented.":[100]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":5},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}