{"id":"https://openalex.org/W2577001942","doi":"https://doi.org/10.1007/s00153-017-0557-4","title":"Interpretability suprema in Peano Arithmetic","display_name":"Interpretability suprema in Peano Arithmetic","publication_year":2017,"publication_date":"2017-05-26","ids":{"openalex":"https://openalex.org/W2577001942","doi":"https://doi.org/10.1007/s00153-017-0557-4","mag":"2577001942"},"language":"en","primary_location":{"id":"doi:10.1007/s00153-017-0557-4","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00153-017-0557-4","pdf_url":"https://link.springer.com/content/pdf/10.1007%2Fs00153-017-0557-4.pdf","source":{"id":"https://openalex.org/S188076996","display_name":"Archive for Mathematical Logic","issn_l":"0933-5846","issn":["0933-5846","1432-0665"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Archive for Mathematical Logic","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007%2Fs00153-017-0557-4.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5023087680","display_name":"Paula Henk","orcid":null},"institutions":[{"id":"https://openalex.org/I887064364","display_name":"University of Amsterdam","ror":"https://ror.org/04dkp9463","country_code":"NL","type":"education","lineage":["https://openalex.org/I887064364"]}],"countries":["NL"],"is_corresponding":true,"raw_author_name":"Paula Henk","raw_affiliation_strings":["Institute for Logic, Language, and Information, University of Amsterdam, Science Park 107, 1098 XG, Amsterdam, The Netherlands"],"affiliations":[{"raw_affiliation_string":"Institute for Logic, Language, and Information, University of Amsterdam, Science Park 107, 1098 XG, Amsterdam, The Netherlands","institution_ids":["https://openalex.org/I887064364"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5056284600","display_name":"Albert Visser","orcid":"https://orcid.org/0000-0001-9452-278X"},"institutions":[{"id":"https://openalex.org/I193662353","display_name":"Utrecht University","ror":"https://ror.org/04pp8hn57","country_code":"NL","type":"education","lineage":["https://openalex.org/I193662353"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Albert Visser","raw_affiliation_strings":["Philosophy, Faculty of Humanities, Utrecht University, Janskerkhof 13, 3512 BL, Utrecht, The Netherlands"],"affiliations":[{"raw_affiliation_string":"Philosophy, Faculty of Humanities, Utrecht University, Janskerkhof 13, 3512 BL, Utrecht, The Netherlands","institution_ids":["https://openalex.org/I193662353"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5023087680"],"corresponding_institution_ids":["https://openalex.org/I887064364"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":0.4157,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.70325027,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"56","issue":"5-6","first_page":"555","last_page":"584"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9830999970436096,"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":0.9830999970436096,"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/T11477","display_name":"Epistemology, Ethics, and Metaphysics","score":0.9355000257492065,"subfield":{"id":"https://openalex.org/subfields/1211","display_name":"Philosophy"},"field":{"id":"https://openalex.org/fields/12","display_name":"Arts and Humanities"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/unary-operation","display_name":"Unary operation","score":0.8773083686828613},{"id":"https://openalex.org/keywords/peano-axioms","display_name":"Peano axioms","score":0.8285481929779053},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8106341361999512},{"id":"https://openalex.org/keywords/infimum-and-supremum","display_name":"Infimum and supremum","score":0.6630208492279053},{"id":"https://openalex.org/keywords/interpretability","display_name":"Interpretability","score":0.5443609952926636},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5399352312088013},{"id":"https://openalex.org/keywords/second-order-arithmetic","display_name":"Second-order arithmetic","score":0.47180476784706116},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.4424838125705719},{"id":"https://openalex.org/keywords/morphism","display_name":"Morphism","score":0.4282994866371155},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.41852933168411255},{"id":"https://openalex.org/keywords/axiom","display_name":"Axiom","score":0.4120425581932068},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.4116678833961487},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2895735502243042},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.11314195394515991},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.10248330235481262}],"concepts":[{"id":"https://openalex.org/C78023250","wikidata":"https://www.wikidata.org/wiki/Q657596","display_name":"Unary operation","level":2,"score":0.8773083686828613},{"id":"https://openalex.org/C97489613","wikidata":"https://www.wikidata.org/wiki/Q842755","display_name":"Peano axioms","level":2,"score":0.8285481929779053},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8106341361999512},{"id":"https://openalex.org/C95611797","wikidata":"https://www.wikidata.org/wiki/Q17502105","display_name":"Infimum and supremum","level":2,"score":0.6630208492279053},{"id":"https://openalex.org/C2781067378","wikidata":"https://www.wikidata.org/wiki/Q17027399","display_name":"Interpretability","level":2,"score":0.5443609952926636},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5399352312088013},{"id":"https://openalex.org/C65148605","wikidata":"https://www.wikidata.org/wiki/Q7442973","display_name":"Second-order arithmetic","level":3,"score":0.47180476784706116},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.4424838125705719},{"id":"https://openalex.org/C137212723","wikidata":"https://www.wikidata.org/wiki/Q1948412","display_name":"Morphism","level":2,"score":0.4282994866371155},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.41852933168411255},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.4120425581932068},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.4116678833961487},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2895735502243042},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.11314195394515991},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.10248330235481262},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"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/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/s00153-017-0557-4","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00153-017-0557-4","pdf_url":"https://link.springer.com/content/pdf/10.1007%2Fs00153-017-0557-4.pdf","source":{"id":"https://openalex.org/S188076996","display_name":"Archive for Mathematical Logic","issn_l":"0933-5846","issn":["0933-5846","1432-0665"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Archive for Mathematical Logic","raw_type":"journal-article"},{"id":"pmh:oai:dare.uva.nl:openaire/7fc7fb90-6036-4ff2-8ead-ac7673e34b84","is_oa":true,"landing_page_url":"https://handle.uba.uva.nl/personal/pure/en/publications/interpretability-suprema-in-peano-arithmetic(7fc7fb90-6036-4ff2-8ead-ac7673e34b84).html","pdf_url":null,"source":{"id":"https://openalex.org/S4306400088","display_name":"UvA-DARE (University of Amsterdam)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I887064364","host_organization_name":"University of Amsterdam","host_organization_lineage":["https://openalex.org/I887064364"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Henk, P & Visser, A 2017, 'Interpretability suprema in Peano Arithmetic', Archive for Mathematical Logic, vol. 56, no. 5-6, pp. 555-584. https://doi.org/10.1007/s00153-017-0557-4","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:uvapub:oai:dare.uva.nl:publications/7fc7fb90-6036-4ff2-8ead-ac7673e34b84","is_oa":true,"landing_page_url":"https://dare.uva.nl/personal/pure/en/publications/interpretability-suprema-in-peano-arithmetic(7fc7fb90-6036-4ff2-8ead-ac7673e34b84).html","pdf_url":"https://dare.uva.nl/personal/pure/en/publications/interpretability-suprema-in-peano-arithmetic(7fc7fb90-6036-4ff2-8ead-ac7673e34b84).html","source":{"id":"https://openalex.org/S4306401843","display_name":"Data Archiving and Networked Services (DANS)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1322597698","host_organization_name":"Royal Netherlands Academy of Arts and Sciences","host_organization_lineage":["https://openalex.org/I1322597698"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Archive for Mathematical Logic, 56(5-6), 555 - 584. Springer New York","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:dspace.library.uu.nl:1874/359437","is_oa":true,"landing_page_url":"https://dspace.library.uu.nl/handle/1874/359437","pdf_url":null,"source":{"id":"https://openalex.org/S4306401649","display_name":"Utrecht University Repository (Utrecht University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I193662353","host_organization_name":"Utrecht University","host_organization_lineage":["https://openalex.org/I193662353"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":{"id":"doi:10.1007/s00153-017-0557-4","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00153-017-0557-4","pdf_url":"https://link.springer.com/content/pdf/10.1007%2Fs00153-017-0557-4.pdf","source":{"id":"https://openalex.org/S188076996","display_name":"Archive for Mathematical Logic","issn_l":"0933-5846","issn":["0933-5846","1432-0665"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Archive for Mathematical Logic","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321008","display_name":"Universiteit van Amsterdam","ror":"https://ror.org/04dkp9463"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2577001942.pdf","grobid_xml":"https://content.openalex.org/works/W2577001942.grobid-xml"},"referenced_works_count":30,"referenced_works":["https://openalex.org/W44069527","https://openalex.org/W840762865","https://openalex.org/W1503684994","https://openalex.org/W1517710889","https://openalex.org/W1571003765","https://openalex.org/W1572451808","https://openalex.org/W1608586249","https://openalex.org/W1911166315","https://openalex.org/W1967494737","https://openalex.org/W1972536043","https://openalex.org/W1974741536","https://openalex.org/W1975810242","https://openalex.org/W2009558863","https://openalex.org/W2016617619","https://openalex.org/W2021219421","https://openalex.org/W2022275578","https://openalex.org/W2028227692","https://openalex.org/W2040404640","https://openalex.org/W2059933820","https://openalex.org/W2064363956","https://openalex.org/W2086963079","https://openalex.org/W2169450060","https://openalex.org/W2270032642","https://openalex.org/W2583152469","https://openalex.org/W2598707475","https://openalex.org/W2743117888","https://openalex.org/W4233830439","https://openalex.org/W4239934161","https://openalex.org/W4255132490","https://openalex.org/W6790579634"],"related_works":["https://openalex.org/W4255069280","https://openalex.org/W2951195380","https://openalex.org/W87599178","https://openalex.org/W2017398442","https://openalex.org/W1991956515","https://openalex.org/W4206411991","https://openalex.org/W4224937162","https://openalex.org/W2023423328","https://openalex.org/W1984065973","https://openalex.org/W2035465455"],"abstract_inverted_index":{"This":[0],"paper":[1],"develops":[2],"the":[3,14,39,54,57,73,86,95,99,109,122,125],"philosophy":[4],"and":[5],"technology":[6],"needed":[7],"for":[8,85,93],"adding":[9,79],"a":[10,36,82,106,117],"supremum":[11,37],"operator":[12],"to":[13,64,71,80],"interpretability":[15,40,87],"logic":[16,127],"$$\\mathsf":[17,23,33,45,60,76,128],"{ILM}$$":[18,61,77],"of":[19,56,75,98,111,124],"Peano":[20],"Arithmetic":[21],"(":[22],"{PA}$$":[24,34,46],").":[25],"It":[26],"is":[27,50,70],"well-known":[28],"that":[29],"any":[30],"theories":[31],"extending":[32],"have":[35],"in":[38,44,53],"ordering.":[41],"While":[42],"provable":[43],",":[47,62],"this":[48],"fact":[49],"not":[51],"reflected":[52],"theorems":[55],"modal":[58],"system":[59],"due":[63],"limited":[65],"expressive":[66],"power.":[67],"Our":[68,102],"goal":[69],"enrich":[72],"language":[74],"by":[78],"it":[81],"new":[83,100],"modality":[84],"supremum.":[88],"We":[89],"explore":[90],"different":[91],"options":[92],"specifying":[94],"exact":[96],"meaning":[97],"modality.":[101],"final":[103],"proposal":[104],"involves":[105],"unary":[107],"operator,":[108],"dual":[110],"which":[112],"can":[113],"be":[114],"seen":[115],"as":[116],"(nonstandard)":[118],"provability":[119,126],"predicate":[120],"satisfying":[121],"axioms":[123],"{GL}$$":[129],".":[130]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}