{"id":"https://openalex.org/W2054442457","doi":"https://doi.org/10.1215/00294527-1722710","title":"Degrees of Relative Provability","display_name":"Degrees of Relative Provability","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W2054442457","doi":"https://doi.org/10.1215/00294527-1722710","mag":"2054442457"},"language":"en","primary_location":{"id":"doi:10.1215/00294527-1722710","is_oa":true,"landing_page_url":"https://doi.org/10.1215/00294527-1722710","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-53/issue-4/Degrees-of-Relative-Provability/10.1215/00294527-1722710.pdf","source":{"id":"https://openalex.org/S78544662","display_name":"Notre Dame Journal of Formal Logic","issn_l":"0029-4527","issn":["0029-4527","1939-0726"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315698","host_organization_name":"Duke University Press","host_organization_lineage":["https://openalex.org/P4310315698","https://openalex.org/P4310315572"],"host_organization_lineage_names":["Duke University Press","Duke University"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Notre Dame Journal of Formal Logic","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-53/issue-4/Degrees-of-Relative-Provability/10.1215/00294527-1722710.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5070121269","display_name":"Mingzhong Cai","orcid":null},"institutions":[{"id":"https://openalex.org/I205783295","display_name":"Cornell University","ror":"https://ror.org/05bnh6r87","country_code":"US","type":"education","lineage":["https://openalex.org/I205783295"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Mingzhong Cai","raw_affiliation_strings":["Department of Mathematics Cornell University Ithaca, New York 14853"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics Cornell University Ithaca, New York 14853","institution_ids":["https://openalex.org/I205783295"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5070121269"],"corresponding_institution_ids":["https://openalex.org/I205783295"],"apc_list":null,"apc_paid":null,"fwci":1.3265,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.83794065,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"53","issue":"4","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9997000098228455,"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/T10126","display_name":"Logic, programming, and type systems","score":0.9997000098228455,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9997000098228455,"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/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9991000294685364,"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/recursion","display_name":"Recursion (computer science)","score":0.8604263067245483},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7748385071754456},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.6496680378913879},{"id":"https://openalex.org/keywords/primitive-recursive-function","display_name":"Primitive recursive function","score":0.6333431601524353},{"id":"https://openalex.org/keywords/double-recursion","display_name":"Double recursion","score":0.4934734106063843},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4674905836582184},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.43049007654190063},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.36761921644210815},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3261844515800476},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2224666178226471}],"concepts":[{"id":"https://openalex.org/C168773036","wikidata":"https://www.wikidata.org/wiki/Q264164","display_name":"Recursion (computer science)","level":2,"score":0.8604263067245483},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7748385071754456},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.6496680378913879},{"id":"https://openalex.org/C9986523","wikidata":"https://www.wikidata.org/wiki/Q1570472","display_name":"Primitive recursive function","level":2,"score":0.6333431601524353},{"id":"https://openalex.org/C139503435","wikidata":"https://www.wikidata.org/wiki/Q5300083","display_name":"Double recursion","level":3,"score":0.4934734106063843},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4674905836582184},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.43049007654190063},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.36761921644210815},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3261844515800476},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2224666178226471},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","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/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1215/00294527-1722710","is_oa":true,"landing_page_url":"https://doi.org/10.1215/00294527-1722710","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-53/issue-4/Degrees-of-Relative-Provability/10.1215/00294527-1722710.pdf","source":{"id":"https://openalex.org/S78544662","display_name":"Notre Dame Journal of Formal Logic","issn_l":"0029-4527","issn":["0029-4527","1939-0726"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315698","host_organization_name":"Duke University Press","host_organization_lineage":["https://openalex.org/P4310315698","https://openalex.org/P4310315572"],"host_organization_lineage_names":["Duke University Press","Duke University"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Notre Dame Journal of Formal Logic","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.ndjfl/1352383227","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.ndjfl/1352383227","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":{"id":"doi:10.1215/00294527-1722710","is_oa":true,"landing_page_url":"https://doi.org/10.1215/00294527-1722710","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-53/issue-4/Degrees-of-Relative-Provability/10.1215/00294527-1722710.pdf","source":{"id":"https://openalex.org/S78544662","display_name":"Notre Dame Journal of Formal Logic","issn_l":"0029-4527","issn":["0029-4527","1939-0726"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315698","host_organization_name":"Duke University Press","host_organization_lineage":["https://openalex.org/P4310315698","https://openalex.org/P4310315572"],"host_organization_lineage_names":["Duke University Press","Duke University"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Notre Dame Journal of Formal Logic","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2360222019","display_name":null,"funder_award_id":"0852811","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G2805389722","display_name":null,"funder_award_id":"085281","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2054442457.pdf","grobid_xml":"https://content.openalex.org/works/W2054442457.grobid-xml"},"referenced_works_count":11,"referenced_works":["https://openalex.org/W96380172","https://openalex.org/W1153502047","https://openalex.org/W1597834884","https://openalex.org/W1989195159","https://openalex.org/W2015272527","https://openalex.org/W2035245701","https://openalex.org/W2081739832","https://openalex.org/W2530006810","https://openalex.org/W2906785358","https://openalex.org/W2907713860","https://openalex.org/W2908250557"],"related_works":["https://openalex.org/W1996792588","https://openalex.org/W2584778959","https://openalex.org/W2074941524","https://openalex.org/W2286072184","https://openalex.org/W4246540581","https://openalex.org/W1845597072","https://openalex.org/W1596057910","https://openalex.org/W2006836388","https://openalex.org/W2095450548","https://openalex.org/W1505802359"],"abstract_inverted_index":{"There":[0],"are":[1],"many":[2],"classical":[3],"connections":[4],"between":[5],"the":[6,14,25,29,36,41,64],"proof-theoretic":[7,54],"strength":[8,27],"of":[9,11,17,28,31,45],"systems":[10],"arithmetic":[12],"and":[13,63],"provable":[15],"totality":[16,30],"recursive":[18,32,46],"functions.":[19],"In":[20],"this":[21,53],"paper":[22],"we":[23],"study":[24],"provability":[26,43],"functions":[33],"by":[34,40],"investigating":[35],"degree":[37,55],"structure":[38,56],"induced":[39],"relative":[42],"order":[44],"algorithms.":[47],"We":[48],"prove":[49],"several":[50],"results":[51],"about":[52],"using":[57],"recursion-theoretic":[58],"techniques":[59],"such":[60],"as":[61],"diagonalization":[62],"Recursion":[65],"Theorem.":[66]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-21T08:09:41.155169","created_date":"2025-10-10T00:00:00"}
