{"id":"https://openalex.org/W2036651904","doi":"https://doi.org/10.1016/s0168-0072(03)00056-3","title":"A second-order system for polytime reasoning based on Gr\u00e4del's theorem","display_name":"A second-order system for polytime reasoning based on Gr\u00e4del's theorem","publication_year":2003,"publication_date":"2003-09-03","ids":{"openalex":"https://openalex.org/W2036651904","doi":"https://doi.org/10.1016/s0168-0072(03)00056-3","mag":"2036651904"},"language":"en","primary_location":{"id":"doi:10.1016/s0168-0072(03)00056-3","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0168-0072(03)00056-3","pdf_url":null,"source":{"id":"https://openalex.org/S172477885","display_name":"Annals of Pure and Applied Logic","issn_l":"0168-0072","issn":["0168-0072","1873-2461"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Annals of Pure and Applied 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/A5034555443","display_name":"Stephen Cook","orcid":null},"institutions":[{"id":"https://openalex.org/I185261750","display_name":"University of Toronto","ror":"https://ror.org/03dbr7087","country_code":"CA","type":"education","lineage":["https://openalex.org/I185261750"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Stephen Cook","raw_affiliation_strings":["Department of Computer Science, University of Toronto, Toronto, Ont., Canada, M5S 3G4"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Toronto, Toronto, Ont., Canada, M5S 3G4","institution_ids":["https://openalex.org/I185261750"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5003773985","display_name":"Antonina Kolokolova","orcid":null},"institutions":[{"id":"https://openalex.org/I185261750","display_name":"University of Toronto","ror":"https://ror.org/03dbr7087","country_code":"CA","type":"education","lineage":["https://openalex.org/I185261750"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Antonina Kolokolova","raw_affiliation_strings":["Department of Computer Science, University of Toronto, Toronto, Ont., Canada, M5S 3G4"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Toronto, Toronto, Ont., Canada, M5S 3G4","institution_ids":["https://openalex.org/I185261750"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5034555443"],"corresponding_institution_ids":["https://openalex.org/I185261750"],"apc_list":{"value":3390,"currency":"USD","value_usd":3390},"apc_paid":null,"fwci":3.3024,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.92405848,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"124","issue":"1-3","first_page":"193","last_page":"231"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9995999932289124,"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"}},"topics":[{"id":"https://openalex.org/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9995999932289124,"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"}},{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9991999864578247,"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"}},{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9987000226974487,"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":0.6910422444343567},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.6105147004127502},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5983937978744507},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5665319561958313},{"id":"https://openalex.org/keywords/reverse-mathematics","display_name":"Reverse mathematics","score":0.5578989386558533},{"id":"https://openalex.org/keywords/corollary","display_name":"Corollary","score":0.5216560363769531},{"id":"https://openalex.org/keywords/second-order-logic","display_name":"Second-order logic","score":0.5122739672660828},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5078640580177307},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.4879741072654724},{"id":"https://openalex.org/keywords/french-horn","display_name":"French horn","score":0.4836200773715973},{"id":"https://openalex.org/keywords/polynomial-hierarchy","display_name":"Polynomial hierarchy","score":0.45741504430770874},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4506514072418213},{"id":"https://openalex.org/keywords/second-order-arithmetic","display_name":"Second-order arithmetic","score":0.42942118644714355},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.4060295820236206},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.38892513513565063},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.34230268001556396},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.30292731523513794},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.18581557273864746},{"id":"https://openalex.org/keywords/axiom","display_name":"Axiom","score":0.15630346536636353},{"id":"https://openalex.org/keywords/description-logic","display_name":"Description logic","score":0.1192295253276825},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.09616687893867493}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6910422444343567},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.6105147004127502},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5983937978744507},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5665319561958313},{"id":"https://openalex.org/C127753061","wikidata":"https://www.wikidata.org/wiki/Q2005236","display_name":"Reverse mathematics","level":3,"score":0.5578989386558533},{"id":"https://openalex.org/C2780012671","wikidata":"https://www.wikidata.org/wiki/Q1343870","display_name":"Corollary","level":2,"score":0.5216560363769531},{"id":"https://openalex.org/C144791301","wikidata":"https://www.wikidata.org/wiki/Q1548746","display_name":"Second-order logic","level":4,"score":0.5122739672660828},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5078640580177307},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4879741072654724},{"id":"https://openalex.org/C152076505","wikidata":"https://www.wikidata.org/wiki/Q1126540","display_name":"French horn","level":2,"score":0.4836200773715973},{"id":"https://openalex.org/C2776013622","wikidata":"https://www.wikidata.org/wiki/Q2103021","display_name":"Polynomial hierarchy","level":3,"score":0.45741504430770874},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4506514072418213},{"id":"https://openalex.org/C65148605","wikidata":"https://www.wikidata.org/wiki/Q7442973","display_name":"Second-order arithmetic","level":3,"score":0.42942118644714355},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.4060295820236206},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.38892513513565063},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.34230268001556396},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.30292731523513794},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.18581557273864746},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.15630346536636353},{"id":"https://openalex.org/C102993220","wikidata":"https://www.wikidata.org/wiki/Q387196","display_name":"Description logic","level":2,"score":0.1192295253276825},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.09616687893867493},{"id":"https://openalex.org/C169896238","wikidata":"https://www.wikidata.org/wiki/Q1644136","display_name":"Higher-order logic","level":3,"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/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C19417346","wikidata":"https://www.wikidata.org/wiki/Q7922","display_name":"Pedagogy","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},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","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/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/s0168-0072(03)00056-3","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0168-0072(03)00056-3","pdf_url":null,"source":{"id":"https://openalex.org/S172477885","display_name":"Annals of Pure and Applied Logic","issn_l":"0168-0072","issn":["0168-0072","1873-2461"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Annals of Pure and Applied Logic","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W87231157","https://openalex.org/W560364776","https://openalex.org/W1585917312","https://openalex.org/W1607926272","https://openalex.org/W1985834822","https://openalex.org/W2045583484","https://openalex.org/W2065251436","https://openalex.org/W2071204190","https://openalex.org/W2075380453","https://openalex.org/W2079745007","https://openalex.org/W2088094394","https://openalex.org/W2091961944","https://openalex.org/W2128026324","https://openalex.org/W2171280299","https://openalex.org/W2399914283","https://openalex.org/W3127113455","https://openalex.org/W3157585079","https://openalex.org/W4206266376","https://openalex.org/W4210843940","https://openalex.org/W4253393488","https://openalex.org/W6858433467"],"related_works":["https://openalex.org/W2047711809","https://openalex.org/W2116579313","https://openalex.org/W2134310526","https://openalex.org/W2086608401","https://openalex.org/W2593141400","https://openalex.org/W2967076817","https://openalex.org/W4213356241","https://openalex.org/W2963686080","https://openalex.org/W2170311073","https://openalex.org/W2155681304"],"abstract_inverted_index":null,"counts_by_year":[{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}