{"id":"https://openalex.org/W1831282203","doi":"https://doi.org/10.1017/s0960129509007695","title":"The Dedekind reals in abstract Stone duality","display_name":"The Dedekind reals in abstract Stone duality","publication_year":2009,"publication_date":"2009-06-08","ids":{"openalex":"https://openalex.org/W1831282203","doi":"https://doi.org/10.1017/s0960129509007695","mag":"1831282203"},"language":"en","primary_location":{"id":"doi:10.1017/s0960129509007695","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0960129509007695","pdf_url":null,"source":{"id":"https://openalex.org/S101766102","display_name":"Mathematical Structures in Computer Science","issn_l":"0960-1295","issn":["0960-1295","1469-8072"],"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":"Mathematical Structures in Computer Science","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5068602858","display_name":"Andrej Bauer","orcid":"https://orcid.org/0000-0001-5378-0547"},"institutions":[{"id":"https://openalex.org/I153976015","display_name":"University of Ljubljana","ror":"https://ror.org/05njb9z20","country_code":"SI","type":"education","lineage":["https://openalex.org/I153976015"]}],"countries":["SI"],"is_corresponding":true,"raw_author_name":"ANDREJ BAUER","raw_affiliation_strings":["University of Ljubljana","University of ljubljana, sloveniaandrej.bauer@andrej.com#TAB#"],"affiliations":[{"raw_affiliation_string":"University of Ljubljana","institution_ids":["https://openalex.org/I153976015"]},{"raw_affiliation_string":"University of ljubljana, sloveniaandrej.bauer@andrej.com#TAB#","institution_ids":["https://openalex.org/I153976015"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5052539592","display_name":"Paul Taylor","orcid":"https://orcid.org/0000-0001-8743-7667"},"institutions":[{"id":"https://openalex.org/I1283236314","display_name":"Thales (Portugal)","ror":"https://ror.org/051w1mx35","country_code":"PT","type":"company","lineage":["https://openalex.org/I1283236314","https://openalex.org/I4210140930"]}],"countries":["PT"],"is_corresponding":false,"raw_author_name":"PAUL TAYLOR","raw_affiliation_strings":["London, United","London, united kingdomdedras@paultaylor.eu#TAB#"],"affiliations":[{"raw_affiliation_string":"London, United","institution_ids":[]},{"raw_affiliation_string":"London, united kingdomdedras@paultaylor.eu#TAB#","institution_ids":["https://openalex.org/I1283236314"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5068602858"],"corresponding_institution_ids":["https://openalex.org/I153976015"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.06140351,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"19","issue":"4","first_page":"757","last_page":"838"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9995999932289124,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9995999932289124,"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/T11151","display_name":"Advanced Topology and Set Theory","score":0.989300012588501,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T13400","display_name":"Mathematical and Theoretical Analysis","score":0.9873999953269958,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/dedekind-cut","display_name":"Dedekind cut","score":0.6622693538665771},{"id":"https://openalex.org/keywords/real-line","display_name":"Real line","score":0.6037682294845581},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5912999510765076},{"id":"https://openalex.org/keywords/computable-analysis","display_name":"Computable analysis","score":0.5515970587730408},{"id":"https://openalex.org/keywords/open-set","display_name":"Open set","score":0.5023939609527588},{"id":"https://openalex.org/keywords/duality","display_name":"Duality (order theory)","score":0.4958437383174896},{"id":"https://openalex.org/keywords/topos-theory","display_name":"Topos theory","score":0.49411728978157043},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.45838209986686707},{"id":"https://openalex.org/keywords/topological-space","display_name":"Topological space","score":0.4549323320388794},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.45113664865493774},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.31406986713409424},{"id":"https://openalex.org/keywords/computability","display_name":"Computability","score":0.28319114446640015}],"concepts":[{"id":"https://openalex.org/C76449584","wikidata":"https://www.wikidata.org/wiki/Q851333","display_name":"Dedekind cut","level":2,"score":0.6622693538665771},{"id":"https://openalex.org/C75432250","wikidata":"https://www.wikidata.org/wiki/Q29654355","display_name":"Real line","level":2,"score":0.6037682294845581},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5912999510765076},{"id":"https://openalex.org/C27318111","wikidata":"https://www.wikidata.org/wiki/Q5157264","display_name":"Computable analysis","level":3,"score":0.5515970587730408},{"id":"https://openalex.org/C42357961","wikidata":"https://www.wikidata.org/wiki/Q213363","display_name":"Open set","level":2,"score":0.5023939609527588},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.4958437383174896},{"id":"https://openalex.org/C182141236","wikidata":"https://www.wikidata.org/wiki/Q2143621","display_name":"Topos theory","level":2,"score":0.49411728978157043},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.45838209986686707},{"id":"https://openalex.org/C81332173","wikidata":"https://www.wikidata.org/wiki/Q179899","display_name":"Topological space","level":2,"score":0.4549323320388794},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.45113664865493774},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.31406986713409424},{"id":"https://openalex.org/C152062344","wikidata":"https://www.wikidata.org/wiki/Q818888","display_name":"Computability","level":2,"score":0.28319114446640015},{"id":"https://openalex.org/C124952713","wikidata":"https://www.wikidata.org/wiki/Q8242","display_name":"Literature","level":1,"score":0.0},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1017/s0960129509007695","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0960129509007695","pdf_url":null,"source":{"id":"https://openalex.org/S101766102","display_name":"Mathematical Structures in Computer Science","issn_l":"0960-1295","issn":["0960-1295","1469-8072"],"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":"Mathematical Structures in Computer Science","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.424.6069","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.424.6069","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/dedras.pdf","raw_type":"text"},{"id":"mag:1831282203","is_oa":false,"landing_page_url":"https://dblp.uni-trier.de/db/conf/cca/cca2005.html#BauerT05","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":60,"referenced_works":["https://openalex.org/W16477519","https://openalex.org/W19739292","https://openalex.org/W22175738","https://openalex.org/W82195733","https://openalex.org/W104853290","https://openalex.org/W119888408","https://openalex.org/W917481348","https://openalex.org/W1480101973","https://openalex.org/W1490729186","https://openalex.org/W1507409515","https://openalex.org/W1512502927","https://openalex.org/W1531550781","https://openalex.org/W1534635720","https://openalex.org/W1582269801","https://openalex.org/W1589741152","https://openalex.org/W1590304156","https://openalex.org/W1597259198","https://openalex.org/W1976398594","https://openalex.org/W1978223406","https://openalex.org/W1994809800","https://openalex.org/W1997051902","https://openalex.org/W1998146115","https://openalex.org/W2007270285","https://openalex.org/W2007293786","https://openalex.org/W2007945990","https://openalex.org/W2011659388","https://openalex.org/W2021068100","https://openalex.org/W2026246736","https://openalex.org/W2031120504","https://openalex.org/W2032719220","https://openalex.org/W2034327355","https://openalex.org/W2034441209","https://openalex.org/W2039977878","https://openalex.org/W2043566933","https://openalex.org/W2049781294","https://openalex.org/W2067914884","https://openalex.org/W2068986168","https://openalex.org/W2074676877","https://openalex.org/W2075490047","https://openalex.org/W2094410575","https://openalex.org/W2098899561","https://openalex.org/W2107560387","https://openalex.org/W2117016770","https://openalex.org/W2119156095","https://openalex.org/W2123630974","https://openalex.org/W2131314484","https://openalex.org/W2137549516","https://openalex.org/W2138898876","https://openalex.org/W2162548412","https://openalex.org/W2461511891","https://openalex.org/W2477597177","https://openalex.org/W2490719060","https://openalex.org/W2611511037","https://openalex.org/W4234797410","https://openalex.org/W4239316923","https://openalex.org/W4243563333","https://openalex.org/W6604929149","https://openalex.org/W6678831985","https://openalex.org/W6680935639","https://openalex.org/W6684029850"],"related_works":["https://openalex.org/W2078425594","https://openalex.org/W2549065385","https://openalex.org/W104853290","https://openalex.org/W2905240033","https://openalex.org/W3115226918","https://openalex.org/W2957828145","https://openalex.org/W2494247423","https://openalex.org/W1498388520","https://openalex.org/W3205783695","https://openalex.org/W2977940537","https://openalex.org/W2152009173","https://openalex.org/W2073858584","https://openalex.org/W1498091675","https://openalex.org/W2039378221","https://openalex.org/W1653897855","https://openalex.org/W2134238565","https://openalex.org/W2133055704","https://openalex.org/W2151814155","https://openalex.org/W2995924551","https://openalex.org/W2093814492"],"abstract_inverted_index":{"Abstract":[0],"Stone":[1],"Duality":[2],"(ASD)":[3],"is":[4,88,97,139],"a":[5,24,34,100,107,161,203],"direct":[6],"axiomatisation":[7],"of":[8,27,33,53,59,65,93,103,122,189,198,206,235],"general":[9],"topology,":[10,86],"in":[11,117,160,208],"contrast":[12],"to":[13,69],"the":[14,60,91,111,123,126,136,154,187,190],"traditional":[15],"and":[16,39,84,141,221,237,240],"all":[17],"other":[18,233],"contemporary":[19],"approaches,":[20],"which":[21,104,185,209],"rely":[22],"on":[23,76,90,166],"prior":[25],"notion":[26],"discrete":[28],"set,":[29],"type":[30],"or":[31,196],"object":[32],"topos.":[35],"ASD":[36,78,96,231],"reconciles":[37],"mathematical":[38],"computational":[40],"viewpoints,":[41],"providing":[42],"an":[43,173],"inherently":[44],"computable":[45,238],"calculus":[46],"that":[47,135,164],"does":[48],"not":[49,193],"sacrifice":[50],"key":[51],"properties":[52],"real":[54,127,191,199],"analysis":[55,67],"such":[56,152],"as":[57,99,110,153,181,194],"compactness":[58],"closed":[61,137],"interval.":[62],"Previous":[63],"theories":[64],"recursive":[66],"failed":[68],"do":[70],"this":[71,167],"because":[72,217],"they":[73],"were":[74],"based":[75],"points;":[77],"succeeds":[79],"because,":[80],"like":[81],"locale":[82],"theory":[83],"formal":[85],"it":[87],"founded":[89],"algebra":[92],"open":[94],"subspaces.":[95],"presented":[98,159],"lambda":[101],"calculus,":[102],"we":[105,178,218,222,229],"provide":[106],"self-contained":[108],"summary,":[109],"foundational":[112,175],"background":[113],"has":[114],"been":[115],"investigated":[116],"earlier":[118],"work.":[119],"The":[120,169],"core":[121],"paper":[124,163],"constructs":[125],"line":[128],"using":[129,148],"two-sided":[130],"Dedekind":[131,183],"cuts.":[132],"We":[133,201],"show":[134],"interval":[138,170],"compact":[140],"overt,":[142],"where":[143],"these":[144],"concepts":[145],"are":[146,158,212],"defined":[147],"quantifiers.":[149],"Further":[150],"topics,":[151],"Intermediate":[155],"Value":[156],"Theorem,":[157],"separate":[162],"builds":[165],"one.":[168],"domain":[171],"plays":[172],"important":[174],"role.":[176],"However,":[177],"see":[179],"intervals":[180],"generalised":[182],"cuts,":[184],"underly":[186],"construction":[188],"line,":[192],"sets":[195],"pairs":[197],"numbers.":[200],"make":[202],"thorough":[204],"study":[205],"arithmetic,":[207],"our":[210],"operations":[211],"more":[213],"complicated":[214],"than":[215],"Moore's,":[216],"work":[219],"constructively,":[220],"also":[223],"consider":[224],"back-to-front":[225],"(Kaucher)":[226],"intervals.":[227],"Finally,":[228],"compare":[230],"with":[232],"systems":[234],"constructive":[236],"topology":[239],"analysis.":[241]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}