{"id":"https://openalex.org/W2032719220","doi":"https://doi.org/10.1016/j.entcs.2004.06.059","title":"Inside Every Model of Abstract Stone Duality Lies an Arithmetic Universe","display_name":"Inside Every Model of Abstract Stone Duality Lies an Arithmetic Universe","publication_year":2005,"publication_date":"2005-03-01","ids":{"openalex":"https://openalex.org/W2032719220","doi":"https://doi.org/10.1016/j.entcs.2004.06.059","mag":"2032719220"},"language":"en","primary_location":{"id":"doi:10.1016/j.entcs.2004.06.059","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.entcs.2004.06.059","pdf_url":null,"source":{"id":"https://openalex.org/S50368787","display_name":"Electronic Notes in Theoretical Computer Science","issn_l":"1571-0661","issn":["1571-0661"],"is_oa":true,"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":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Electronic Notes in Theoretical Computer Science","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://doi.org/10.1016/j.entcs.2004.06.059","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5052539592","display_name":"Paul Taylor","orcid":"https://orcid.org/0000-0001-8743-7667"},"institutions":[{"id":"https://openalex.org/I28407311","display_name":"University of Manchester","ror":"https://ror.org/027m9bs27","country_code":"GB","type":"education","lineage":["https://openalex.org/I28407311"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Paul Taylor","raw_affiliation_strings":["Department of Computer Science, University of Manchester"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Manchester","institution_ids":["https://openalex.org/I28407311"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5052539592"],"corresponding_institution_ids":["https://openalex.org/I28407311"],"apc_list":null,"apc_paid":null,"fwci":2.0198,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.86686504,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"122","issue":null,"first_page":"247","last_page":"296"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9986000061035156,"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":0.9986000061035156,"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":0.9955000281333923,"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":0.9934999942779541,"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/mathematics","display_name":"Mathematics","score":0.7465327382087708},{"id":"https://openalex.org/keywords/disjoint-sets","display_name":"Disjoint sets","score":0.6846378445625305},{"id":"https://openalex.org/keywords/subcategory","display_name":"Subcategory","score":0.5919941663742065},{"id":"https://openalex.org/keywords/axiom","display_name":"Axiom","score":0.5438700914382935},{"id":"https://openalex.org/keywords/monoid","display_name":"Monoid","score":0.5393787026405334},{"id":"https://openalex.org/keywords/semilattice","display_name":"Semilattice","score":0.4956275224685669},{"id":"https://openalex.org/keywords/universe","display_name":"Universe","score":0.48711323738098145},{"id":"https://openalex.org/keywords/quotient","display_name":"Quotient","score":0.470253586769104},{"id":"https://openalex.org/keywords/axiom-of-choice","display_name":"Axiom of choice","score":0.45560023188591003},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.41487500071525574},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.37297502160072327},{"id":"https://openalex.org/keywords/semigroup","display_name":"Semigroup","score":0.15306884050369263},{"id":"https://openalex.org/keywords/set-theory","display_name":"Set theory","score":0.13965079188346863},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1198149025440216},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.11681711673736572}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7465327382087708},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.6846378445625305},{"id":"https://openalex.org/C2780617661","wikidata":"https://www.wikidata.org/wiki/Q541563","display_name":"Subcategory","level":2,"score":0.5919941663742065},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.5438700914382935},{"id":"https://openalex.org/C206901836","wikidata":"https://www.wikidata.org/wiki/Q208237","display_name":"Monoid","level":2,"score":0.5393787026405334},{"id":"https://openalex.org/C132170107","wikidata":"https://www.wikidata.org/wiki/Q834585","display_name":"Semilattice","level":3,"score":0.4956275224685669},{"id":"https://openalex.org/C84999194","wikidata":"https://www.wikidata.org/wiki/Q1","display_name":"Universe","level":2,"score":0.48711323738098145},{"id":"https://openalex.org/C199422724","wikidata":"https://www.wikidata.org/wiki/Q41118","display_name":"Quotient","level":2,"score":0.470253586769104},{"id":"https://openalex.org/C151797676","wikidata":"https://www.wikidata.org/wiki/Q179692","display_name":"Axiom of choice","level":4,"score":0.45560023188591003},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.41487500071525574},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.37297502160072327},{"id":"https://openalex.org/C207405024","wikidata":"https://www.wikidata.org/wiki/Q207348","display_name":"Semigroup","level":2,"score":0.15306884050369263},{"id":"https://openalex.org/C153046414","wikidata":"https://www.wikidata.org/wiki/Q12482","display_name":"Set theory","level":3,"score":0.13965079188346863},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1198149025440216},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.11681711673736572},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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/C44870925","wikidata":"https://www.wikidata.org/wiki/Q37547","display_name":"Astrophysics","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:10.1016/j.entcs.2004.06.059","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.entcs.2004.06.059","pdf_url":null,"source":{"id":"https://openalex.org/S50368787","display_name":"Electronic Notes in Theoretical Computer Science","issn_l":"1571-0661","issn":["1571-0661"],"is_oa":true,"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":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Electronic Notes in Theoretical Computer Science","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.619.6437","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.619.6437","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.paultaylor.eu/ASD/insema/insema.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1016/j.entcs.2004.06.059","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.entcs.2004.06.059","pdf_url":null,"source":{"id":"https://openalex.org/S50368787","display_name":"Electronic Notes in Theoretical Computer Science","issn_l":"1571-0661","issn":["1571-0661"],"is_oa":true,"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":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Electronic Notes in Theoretical Computer Science","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.41999998688697815}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W22175738","https://openalex.org/W82195733","https://openalex.org/W215189873","https://openalex.org/W415181100","https://openalex.org/W1773829243","https://openalex.org/W1831282203","https://openalex.org/W1977571882","https://openalex.org/W1997051902","https://openalex.org/W2032386884","https://openalex.org/W2032719220","https://openalex.org/W2033225733","https://openalex.org/W2049362364","https://openalex.org/W2060984753","https://openalex.org/W2078425594","https://openalex.org/W2088523838","https://openalex.org/W2107560387","https://openalex.org/W2138898876","https://openalex.org/W2157471937","https://openalex.org/W2162548412","https://openalex.org/W2324455841","https://openalex.org/W2480722803","https://openalex.org/W3177299375","https://openalex.org/W4285719527","https://openalex.org/W6638006809","https://openalex.org/W6642345100","https://openalex.org/W6644951578","https://openalex.org/W6787237226"],"related_works":["https://openalex.org/W4300717381","https://openalex.org/W3196726381","https://openalex.org/W2054722332","https://openalex.org/W2124484802","https://openalex.org/W2930972157","https://openalex.org/W1991377879","https://openalex.org/W2088306712","https://openalex.org/W3006395458","https://openalex.org/W2171612773","https://openalex.org/W2988306874"],"abstract_inverted_index":{"The":[0],"first":[1],"paper":[2],"published":[3],"on":[4,72,97],"Abstract":[5],"Stone":[6],"Duality":[7],"showed":[8],"that":[9,49],"the":[10],"overt":[11,74],"discrete":[12,75],"objects":[13],"(those":[14],"admitting":[15],"\u2203":[16],"and":[17,32,65,108,110],"=":[18],"internally)":[19],"form":[20],"a":[21,24,58,66,91,98,127],"pretopos,":[22],"i.e.":[23],"category":[25],"with":[26,94],"finite":[27,78],"limits,":[28],"stable":[29,33],"disjoint":[30],"coproducts":[31],"effective":[34],"quotients":[35],"of":[36,62,70,87,118,126],"equivalence":[37],"relations.":[38],"Using":[39],"an":[40,54],"N-indexed":[41],"least":[42],"fixed":[43],"point":[44],"axiom,":[45],"here":[46],"we":[47],"show":[48],"this":[50,120],"full":[51],"subcategory":[52],"is":[53,80],"arithmetic":[55],"universe,":[56],"having":[57],"free":[59,67],"semilattice":[60],"(\u201ccollection":[61,69],"Kuratowski-finite":[63],"subsets\u201d)":[64],"monoid":[68],"lists\u201d)":[71],"any":[73],"object.":[76],"Each":[77],"subset":[79],"represented":[81],"by":[82],"its":[83],"pair":[84],"(\u25a1,":[85],"\u25ca)":[86],"modal":[88],"operators,":[89],"although":[90],"tight":[92],"correspondence":[93],"these":[95],"depends":[96],"stronger":[99],"Scott-continuity":[100],"axiom.":[101],"Topologically,":[102],"such":[103],"subsets":[104],"are":[105],"both":[106],"compact":[107],"open":[109,114],"also":[111],"involve":[112],"proper":[113],"maps.":[115],"In":[116],"applications":[117],"ASD":[119],"can":[121],"eliminate":[122],"lists":[123],"in":[124],"favour":[125],"continuation-passing":[128],"interpretation.":[129]},"counts_by_year":[{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
