{"id":"https://openalex.org/W2079956582","doi":"https://doi.org/10.1215/00294527-2008-029","title":"On Interpretability in the Theory of Concatenation","display_name":"On Interpretability in the Theory of Concatenation","publication_year":2009,"publication_date":"2009-01-01","ids":{"openalex":"https://openalex.org/W2079956582","doi":"https://doi.org/10.1215/00294527-2008-029","mag":"2079956582"},"language":"en","primary_location":{"id":"doi:10.1215/00294527-2008-029","is_oa":true,"landing_page_url":"https://doi.org/10.1215/00294527-2008-029","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-50/issue-1/On-Interpretability-in-the-Theory-of-Concatenation/10.1215/00294527-2008-029.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-50/issue-1/On-Interpretability-in-the-Theory-of-Concatenation/10.1215/00294527-2008-029.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5055871345","display_name":"V\u00edt\u011bzslav \u0160vejdar","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"V\u00edt\u011bzslav \u0160vejdar","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5055871345"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.7618,"has_fulltext":true,"cited_by_count":39,"citation_normalized_percentile":{"value":0.84583509,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":"50","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","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/T11727","display_name":"Advanced Algebra and Logic","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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9972000122070312,"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":0.9926999807357788,"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/concatenation","display_name":"Concatenation (mathematics)","score":0.9182051420211792},{"id":"https://openalex.org/keywords/interpretability","display_name":"Interpretability","score":0.7532616257667542},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5556250214576721},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.47789204120635986},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.40157780051231384},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.35243356227874756},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3374401926994324},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3321843147277832},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.26002025604248047},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.16097086668014526}],"concepts":[{"id":"https://openalex.org/C87619178","wikidata":"https://www.wikidata.org/wiki/Q126002","display_name":"Concatenation (mathematics)","level":2,"score":0.9182051420211792},{"id":"https://openalex.org/C2781067378","wikidata":"https://www.wikidata.org/wiki/Q17027399","display_name":"Interpretability","level":2,"score":0.7532616257667542},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5556250214576721},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.47789204120635986},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.40157780051231384},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.35243356227874756},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3374401926994324},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3321843147277832},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.26002025604248047},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.16097086668014526}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1215/00294527-2008-029","is_oa":true,"landing_page_url":"https://doi.org/10.1215/00294527-2008-029","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-50/issue-1/On-Interpretability-in-the-Theory-of-Concatenation/10.1215/00294527-2008-029.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/1232375164","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.ndjfl/1232375164","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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.92.4353","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.92.4353","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www1.cuni.cz/~svejdar/papers/sv_tc.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1215/00294527-2008-029","is_oa":true,"landing_page_url":"https://doi.org/10.1215/00294527-2008-029","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-50/issue-1/On-Interpretability-in-the-Theory-of-Concatenation/10.1215/00294527-2008-029.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":[],"funders":[{"id":"https://openalex.org/F4320310260","display_name":"University of Notre Dame","ror":"https://ror.org/00mkhxb43"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2079956582.pdf","grobid_xml":"https://content.openalex.org/works/W2079956582.grobid-xml"},"referenced_works_count":9,"referenced_works":["https://openalex.org/W1517710889","https://openalex.org/W1776780778","https://openalex.org/W1953960400","https://openalex.org/W1962276536","https://openalex.org/W2032467105","https://openalex.org/W2035476945","https://openalex.org/W2062842033","https://openalex.org/W2123447690","https://openalex.org/W3137241174"],"related_works":["https://openalex.org/W2905433371","https://openalex.org/W4361193272","https://openalex.org/W4310278675","https://openalex.org/W2806259446","https://openalex.org/W2963326959","https://openalex.org/W4311431240","https://openalex.org/W4312407344","https://openalex.org/W4384115502","https://openalex.org/W2946585142","https://openalex.org/W3120719177"],"abstract_inverted_index":{"We":[0],"prove":[1],"that":[2,32],"a":[3,38],"variant":[4],"of":[5,17,57],"Robinson":[6],"arithmetic":[7],"Q":[8,25,45],"with":[9],"nontotal":[10,33],"operations":[11],"is":[12,26,46,54],"interpretable":[13,30,47],"in":[14,31,48],"the":[15,42],"theory":[16],"concatenation":[18],"TC":[19,49,58],"introduced":[20],"by":[21],"A.":[22],"Grzegorczyk.":[23],"Since":[24],"known":[27],"to":[28,41],"be":[29],"variant,":[34],"our":[35],"result":[36],"gives":[37],"positive":[39],"answer":[40],"problem":[43],"whether":[44],".":[50,59],"An":[51],"immediate":[52],"consequence":[53],"essential":[55],"undecidability":[56]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":18},{"year":2017,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":3},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}