{"id":"https://openalex.org/W2527970226","doi":"https://doi.org/10.1017/s1755020318000461","title":"A NOTE ON THE REVERSE MATHEMATICS OF THE SORITES","display_name":"A NOTE ON THE REVERSE MATHEMATICS OF THE SORITES","publication_year":2018,"publication_date":"2018-12-07","ids":{"openalex":"https://openalex.org/W2527970226","doi":"https://doi.org/10.1017/s1755020318000461","mag":"2527970226"},"language":"en","primary_location":{"id":"doi:10.1017/s1755020318000461","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s1755020318000461","pdf_url":null,"source":{"id":"https://openalex.org/S24077076","display_name":"The Review of Symbolic Logic","issn_l":"1755-0203","issn":["1755-0203","1755-0211"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Review of Symbolic Logic","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1610.00213","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"DAMIR D. DZHAFAROV","orcid":null},"institutions":[{"id":"https://openalex.org/I140172145","display_name":"University of Connecticut","ror":"https://ror.org/02der9h97","country_code":"US","type":"education","lineage":["https://openalex.org/I140172145"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"DAMIR D. DZHAFAROV","raw_affiliation_strings":["Department of Mathematics, University of Connecticut"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Connecticut","institution_ids":["https://openalex.org/I140172145"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I140172145"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.02730714,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"12","issue":"1","first_page":"30","last_page":"36"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13400","display_name":"Mathematical and Theoretical Analysis","score":0.4544000029563904,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T13400","display_name":"Mathematical and Theoretical Analysis","score":0.4544000029563904,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.10080000013113022,"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/T10126","display_name":"Logic, programming, and type systems","score":0.09019999951124191,"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/constructive","display_name":"Constructive","score":0.7368000149726868},{"id":"https://openalex.org/keywords/social-connectedness","display_name":"Social connectedness","score":0.6563000082969666},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5909000039100647},{"id":"https://openalex.org/keywords/pairwise-comparison","display_name":"Pairwise comparison","score":0.5303000211715698},{"id":"https://openalex.org/keywords/element","display_name":"Element (criminal law)","score":0.5174999833106995},{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.46299999952316284},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4311000108718872}],"concepts":[{"id":"https://openalex.org/C2778701210","wikidata":"https://www.wikidata.org/wiki/Q28130034","display_name":"Constructive","level":3,"score":0.7368000149726868},{"id":"https://openalex.org/C201943243","wikidata":"https://www.wikidata.org/wiki/Q7551008","display_name":"Social connectedness","level":2,"score":0.6563000082969666},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5909000039100647},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.557699978351593},{"id":"https://openalex.org/C184898388","wikidata":"https://www.wikidata.org/wiki/Q1435712","display_name":"Pairwise comparison","level":2,"score":0.5303000211715698},{"id":"https://openalex.org/C200288055","wikidata":"https://www.wikidata.org/wiki/Q2621792","display_name":"Element (criminal law)","level":2,"score":0.5174999833106995},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.46299999952316284},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4311000108718872},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.398499995470047},{"id":"https://openalex.org/C202854965","wikidata":"https://www.wikidata.org/wiki/Q3044470","display_name":"Constructive proof","level":2,"score":0.37599998712539673},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3716999888420105},{"id":"https://openalex.org/C153046414","wikidata":"https://www.wikidata.org/wiki/Q12482","display_name":"Set theory","level":3,"score":0.3472000062465668},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3465000092983246},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.2971999943256378},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.296099990606308},{"id":"https://openalex.org/C199185054","wikidata":"https://www.wikidata.org/wiki/Q552299","display_name":"Chain (unit)","level":2,"score":0.2825999855995178},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.27059999108314514},{"id":"https://openalex.org/C2776436953","wikidata":"https://www.wikidata.org/wiki/Q5163215","display_name":"Consistency (knowledge bases)","level":2,"score":0.26829999685287476},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.25769999623298645}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1017/s1755020318000461","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s1755020318000461","pdf_url":null,"source":{"id":"https://openalex.org/S24077076","display_name":"The Review of Symbolic Logic","issn_l":"1755-0203","issn":["1755-0203","1755-0211"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Review of Symbolic Logic","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1610.00213","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1610.00213","pdf_url":"https://arxiv.org/pdf/1610.00213","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"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":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1610.00213","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1610.00213","pdf_url":"https://arxiv.org/pdf/1610.00213","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"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":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W19086289","https://openalex.org/W123245502","https://openalex.org/W1595235134","https://openalex.org/W1995107123","https://openalex.org/W2040795526","https://openalex.org/W2071956244","https://openalex.org/W2141268006","https://openalex.org/W3030493957","https://openalex.org/W4229690001","https://openalex.org/W4238214510"],"related_works":[],"abstract_inverted_index":{"Abstract":[0],"Sorites":[1],"is":[2,68,146,156,173],"an":[3,30],"ancient":[4],"piece":[5],"of":[6,18,26,44,75,82,91,100,139,144,154,171,178],"paradoxical":[7],"reasoning":[8],"pertaining":[9],"to":[10,121,158],"sets":[11],"with":[12,62],"the":[13,19,39,105,128,137,142,152,169],"following":[14],"properties:":[15],"(Supervenience)":[16],"elements":[17,40,61],"set":[20,25],"are":[21,38,107],"mapped":[22],"into":[23,54],"some":[24,42],"\u201cattributes\u201d;":[27],"(Tolerance)":[28],"if":[29,66],"element":[31],"has":[32],"a":[33,85,116,165],"given":[34],"attribute":[35],"then":[36,70],"so":[37],"in":[41,111,136,148,164],"vicinity":[43],"this":[45,112],"element;":[46],"and":[47,77],"(Connectedness)":[48],"such":[49],"vicinities":[50],"can":[51],"be":[52],"arranged":[53],"pairwise":[55],"overlapping":[56],"finite":[57],"chains":[58],"connecting":[59],"two":[60,98],"different":[63,117,131],"attributes.":[64],"Obviously,":[65],"Superveneince":[67],"assumed,":[69],"(1)":[71,145,172],"Tolerance":[72],"implies":[73,80],"lack":[74,81],"Connectedness,":[76],"(2)":[78,155],"Connectedness":[79],"Tolerance.":[83],"Using":[84],"very":[86],"general":[87],"but":[88,110],"precise":[89,167],"definition":[90],"\u201cvicinity\u201d,":[92],"Dzhafarov":[93,95],"&amp;":[94],"(2010)":[96],"offered":[97],"formalizations":[99,106,129],"these":[101],"mutual":[102],"contrapositions.":[103],"Mathematically,":[104],"equally":[108],"valid,":[109],"paper,":[113],"we":[114,125],"offer":[115],"basis":[118],"by":[119],"which":[120],"compare":[122],"them.":[123],"Namely,":[124],"show":[126],"that":[127,177],"have":[130],"proof-theoretic":[132],"strengths":[133],"when":[134],"measured":[135],"framework":[138],"reverse":[140],"mathematics:":[141],"formalization":[143,153],"provable":[147],"$RC{A_0}$":[149,161],",":[150],"while":[151],"equivalent":[157],"$AC{A_0}$":[159],"over":[160],".":[162],"Thus,":[163],"certain":[166],"sense,":[168],"approach":[170],"more":[174],"constructive":[175],"than":[176],"(2).":[179]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2016-10-14T00:00:00"}
