{"id":"https://openalex.org/W2129959868","doi":"https://doi.org/10.1002/malq.19970430315","title":"Rudimentary Languages and Second\u2010Order Logic","display_name":"Rudimentary Languages and Second\u2010Order Logic","publication_year":1997,"publication_date":"1997-01-01","ids":{"openalex":"https://openalex.org/W2129959868","doi":"https://doi.org/10.1002/malq.19970430315","mag":"2129959868"},"language":"en","primary_location":{"id":"doi:10.1002/malq.19970430315","is_oa":false,"landing_page_url":"https://doi.org/10.1002/malq.19970430315","pdf_url":null,"source":{"id":"https://openalex.org/S172351290","display_name":"Mathematical logic quarterly","issn_l":"0942-5616","issn":["0942-5616","1521-3870"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Logic Quarterly","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/A5018429744","display_name":"Malika More","orcid":null},"institutions":[{"id":"https://openalex.org/I98702875","display_name":"Universit\u00e9 de Caen Normandie","ror":"https://ror.org/051kpcy16","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210105918","https://openalex.org/I98702875"]},{"id":"https://openalex.org/I3019441195","display_name":"Laboratoire de Math\u00e9matiques d'Orsay","ror":"https://ror.org/03ab0zs98","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I277688954","https://openalex.org/I3019441195"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Malika More","raw_affiliation_strings":["GRAL, De\u0301partement de mathe\u0301matiques, Universite\u0301 de Caen, 14032 Caen Cedex, France","GRAL, D\u00e9partement de math\u00e9matiques, Universit\u00e9 de Caen, 14032 Caen Cedex, France"],"affiliations":[{"raw_affiliation_string":"GRAL, De\u0301partement de mathe\u0301matiques, Universite\u0301 de Caen, 14032 Caen Cedex, France","institution_ids":["https://openalex.org/I3019441195","https://openalex.org/I98702875"]},{"raw_affiliation_string":"GRAL, D\u00e9partement de math\u00e9matiques, Universit\u00e9 de Caen, 14032 Caen Cedex, France","institution_ids":["https://openalex.org/I3019441195"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5025043872","display_name":"Fr\u00e9d\u00e9ric Olive","orcid":"https://orcid.org/0000-0002-3552-5566"},"institutions":[{"id":"https://openalex.org/I4210139483","display_name":"GREYC","ror":"https://ror.org/043749971","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I194210350","https://openalex.org/I4210105918","https://openalex.org/I4210105918","https://openalex.org/I4210139483","https://openalex.org/I4210159245","https://openalex.org/I98702875"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Fr\u00e9d\u00e9ric Olive","raw_affiliation_strings":["GREYC, De\u0301partement d'informatique, Universite\u0301 de Caen, 14032 Caen Cedex, France","GREYC, D\u00e9partement d'informatique, Universit\u00e9 de Caen, 14032 Caen Cedex, France"],"affiliations":[{"raw_affiliation_string":"GREYC, De\u0301partement d'informatique, Universite\u0301 de Caen, 14032 Caen Cedex, France","institution_ids":["https://openalex.org/I4210139483"]},{"raw_affiliation_string":"GREYC, D\u00e9partement d'informatique, Universit\u00e9 de Caen, 14032 Caen Cedex, France","institution_ids":["https://openalex.org/I4210139483"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5018429744"],"corresponding_institution_ids":["https://openalex.org/I3019441195","https://openalex.org/I98702875"],"apc_list":{"value":2630,"currency":"USD","value_usd":2630},"apc_paid":null,"fwci":0.5024,"has_fulltext":false,"cited_by_count":14,"citation_normalized_percentile":{"value":0.6793675,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"43","issue":"3","first_page":"419","last_page":"426"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.9983000159263611,"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/T11567","display_name":"semigroups and automata theory","score":0.9983000159263611,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.9966999888420105,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9965000152587891,"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/mathematics","display_name":"Mathematics","score":0.6679961085319519},{"id":"https://openalex.org/keywords/descriptive-complexity-theory","display_name":"Descriptive complexity theory","score":0.6064966320991516},{"id":"https://openalex.org/keywords/recursion","display_name":"Recursion (computer science)","score":0.5616945028305054},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.5616520047187805},{"id":"https://openalex.org/keywords/complexity-class","display_name":"Complexity class","score":0.520629346370697},{"id":"https://openalex.org/keywords/second-order-logic","display_name":"Second-order logic","score":0.5056431293487549},{"id":"https://openalex.org/keywords/hierarchy","display_name":"Hierarchy","score":0.46893930435180664},{"id":"https://openalex.org/keywords/first-order-logic","display_name":"First-order logic","score":0.46682968735694885},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.45370998978614807},{"id":"https://openalex.org/keywords/formal-language","display_name":"Formal language","score":0.45272377133369446},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.42799150943756104},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.35857391357421875},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3547600507736206},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3444839119911194},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2949873208999634},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.2566005289554596},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2547191381454468},{"id":"https://openalex.org/keywords/higher-order-logic","display_name":"Higher-order logic","score":0.24436864256858826},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.20396259427070618},{"id":"https://openalex.org/keywords/description-logic","display_name":"Description logic","score":0.13805410265922546},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.11526185274124146}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6679961085319519},{"id":"https://openalex.org/C133142742","wikidata":"https://www.wikidata.org/wiki/Q1200755","display_name":"Descriptive complexity theory","level":3,"score":0.6064966320991516},{"id":"https://openalex.org/C168773036","wikidata":"https://www.wikidata.org/wiki/Q264164","display_name":"Recursion (computer science)","level":2,"score":0.5616945028305054},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.5616520047187805},{"id":"https://openalex.org/C39637292","wikidata":"https://www.wikidata.org/wiki/Q908207","display_name":"Complexity class","level":3,"score":0.520629346370697},{"id":"https://openalex.org/C144791301","wikidata":"https://www.wikidata.org/wiki/Q1548746","display_name":"Second-order logic","level":4,"score":0.5056431293487549},{"id":"https://openalex.org/C31170391","wikidata":"https://www.wikidata.org/wiki/Q188619","display_name":"Hierarchy","level":2,"score":0.46893930435180664},{"id":"https://openalex.org/C100481476","wikidata":"https://www.wikidata.org/wiki/Q4055684","display_name":"First-order logic","level":2,"score":0.46682968735694885},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.45370998978614807},{"id":"https://openalex.org/C146072743","wikidata":"https://www.wikidata.org/wiki/Q192161","display_name":"Formal language","level":2,"score":0.45272377133369446},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.42799150943756104},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.35857391357421875},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3547600507736206},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3444839119911194},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2949873208999634},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.2566005289554596},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2547191381454468},{"id":"https://openalex.org/C169896238","wikidata":"https://www.wikidata.org/wiki/Q1644136","display_name":"Higher-order logic","level":3,"score":0.24436864256858826},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.20396259427070618},{"id":"https://openalex.org/C102993220","wikidata":"https://www.wikidata.org/wiki/Q387196","display_name":"Description logic","level":2,"score":0.13805410265922546},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.11526185274124146},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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},{"id":"https://openalex.org/C34447519","wikidata":"https://www.wikidata.org/wiki/Q179522","display_name":"Market economy","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/malq.19970430315","is_oa":false,"landing_page_url":"https://doi.org/10.1002/malq.19970430315","pdf_url":null,"source":{"id":"https://openalex.org/S172351290","display_name":"Mathematical logic quarterly","issn_l":"0942-5616","issn":["0942-5616","1521-3870"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Logic Quarterly","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.6600000262260437,"display_name":"Quality Education","id":"https://metadata.un.org/sdg/4"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W1535924067","https://openalex.org/W1970629906","https://openalex.org/W2004663163","https://openalex.org/W2035004935","https://openalex.org/W2035476945","https://openalex.org/W2044122859","https://openalex.org/W2065251436","https://openalex.org/W2078123020","https://openalex.org/W2401610261","https://openalex.org/W2562830775","https://openalex.org/W3127113455","https://openalex.org/W4205178514"],"related_works":["https://openalex.org/W2964237202","https://openalex.org/W3094951835","https://openalex.org/W2168681835","https://openalex.org/W1560572178","https://openalex.org/W1543965609","https://openalex.org/W2963635167","https://openalex.org/W1831301291","https://openalex.org/W2069462712","https://openalex.org/W2017143384","https://openalex.org/W2962733163"],"abstract_inverted_index":{"Abstract":[0],"The":[1],"aim":[2],"of":[3,86,93],"this":[4,46],"paper":[5],"is":[6],"to":[7,35,52,54],"point":[8],"out":[9],"the":[10,27,30,39,43,67,76],"equivalence":[11],"between":[12,70],"three":[13],"notions":[14,79],"respectively":[15],"issued":[16],"from":[17,110],"recursion":[18],"theory,":[19],"computational":[20,111],"complexity":[21,47],"and":[22,89,104],"finite":[23],"model":[24],"theory.":[25],"One":[26],"one":[28],"hand,":[29,45],"rudimentary":[31,87],"languages":[32,88],"are":[33],"known":[34],"be":[36,50],"characterized":[37],"by":[38,80],"linear":[40],"hierarchy.":[41],"On":[42],"other":[44],"class":[48],"can":[49],"proved":[51],"correspond":[53],"monadic":[55],"second\u2010order":[56,94],"logic":[57,95],"with":[58],"addition.":[59],"Our":[60],"viewpoint":[61],"sheds":[62],"some":[63],"new":[64],"light":[65],"on":[66],"close":[68],"connection":[69],"these":[71,97],"domains:":[72],"We":[73,99],"bring":[74],"together":[75],"two":[77],"extremal":[78],"providing":[81],"a":[82,90],"direct":[83],"logical":[84],"characterization":[85],"representation":[91],"result":[92],"into":[96],"languages.":[98],"use":[100],"natural":[101],"arithmetical":[102],"tools,":[103],"our":[105],"proofs":[106],"contain":[107],"no":[108],"ingredient":[109],"complexity.":[112]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-01-15T23:16:33.117629","created_date":"2025-10-10T00:00:00"}
