{"id":"https://openalex.org/W2114953769","doi":"https://doi.org/10.2307/421098","title":"Domains for Computation in Mathematics, Physics and Exact Real Arithmetic","display_name":"Domains for Computation in Mathematics, Physics and Exact Real Arithmetic","publication_year":1997,"publication_date":"1997-12-01","ids":{"openalex":"https://openalex.org/W2114953769","doi":"https://doi.org/10.2307/421098","mag":"2114953769"},"language":"en","primary_location":{"id":"doi:10.2307/421098","is_oa":false,"landing_page_url":"https://doi.org/10.2307/421098","pdf_url":null,"source":{"id":"https://openalex.org/S130801046","display_name":"Bulletin of Symbolic Logic","issn_l":"1079-8986","issn":["1079-8986","1943-5894"],"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":"Bulletin of Symbolic Logic","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/A5058087229","display_name":"Abbas Edalat","orcid":"https://orcid.org/0000-0002-6211-1991"},"institutions":[{"id":"https://openalex.org/I47508984","display_name":"Imperial College London","ror":"https://ror.org/041kmwe10","country_code":"GB","type":"education","lineage":["https://openalex.org/I47508984"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Abbas Edalat","raw_affiliation_strings":["Department of Computing, Imperial College of Science, Technology and Medicine, 180 Queen's Gate London SW7 2BZ, UK.E-mail:","Department of Computing, Imperial College of Science, Technology and Medicine, 180 Queen's Gate London SW7 2BZ, UK. E-mail/i: ae@doc.ic.ac.uk"],"affiliations":[{"raw_affiliation_string":"Department of Computing, Imperial College of Science, Technology and Medicine, 180 Queen's Gate London SW7 2BZ, UK.E-mail:","institution_ids":["https://openalex.org/I47508984"]},{"raw_affiliation_string":"Department of Computing, Imperial College of Science, Technology and Medicine, 180 Queen's Gate London SW7 2BZ, UK. E-mail/i: ae@doc.ic.ac.uk","institution_ids":["https://openalex.org/I47508984"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5058087229"],"corresponding_institution_ids":["https://openalex.org/I47508984"],"apc_list":null,"apc_paid":null,"fwci":8.7977,"has_fulltext":false,"cited_by_count":132,"citation_normalized_percentile":{"value":0.98924008,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"3","issue":"4","first_page":"401","last_page":"452"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9994999766349792,"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9994999766349792,"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/T12162","display_name":"Cellular Automata and Applications","score":0.9819999933242798,"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":0.9768000245094299,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/iterated-function-system","display_name":"Iterated function system","score":0.6935006976127625},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6588797569274902},{"id":"https://openalex.org/keywords/second-order-arithmetic","display_name":"Second-order arithmetic","score":0.6186416149139404},{"id":"https://openalex.org/keywords/number-theory","display_name":"Number theory","score":0.4365927278995514},{"id":"https://openalex.org/keywords/real-line","display_name":"Real line","score":0.4111808240413666},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3936395049095154},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3846988081932068},{"id":"https://openalex.org/keywords/fractal","display_name":"Fractal","score":0.34011566638946533},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2852756977081299},{"id":"https://openalex.org/keywords/peano-axioms","display_name":"Peano axioms","score":0.17751330137252808},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1254948079586029}],"concepts":[{"id":"https://openalex.org/C168460219","wikidata":"https://www.wikidata.org/wiki/Q1502167","display_name":"Iterated function system","level":3,"score":0.6935006976127625},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6588797569274902},{"id":"https://openalex.org/C65148605","wikidata":"https://www.wikidata.org/wiki/Q7442973","display_name":"Second-order arithmetic","level":3,"score":0.6186416149139404},{"id":"https://openalex.org/C169654258","wikidata":"https://www.wikidata.org/wiki/Q12479","display_name":"Number theory","level":2,"score":0.4365927278995514},{"id":"https://openalex.org/C75432250","wikidata":"https://www.wikidata.org/wiki/Q29654355","display_name":"Real line","level":2,"score":0.4111808240413666},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3936395049095154},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3846988081932068},{"id":"https://openalex.org/C40636538","wikidata":"https://www.wikidata.org/wiki/Q81392","display_name":"Fractal","level":2,"score":0.34011566638946533},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2852756977081299},{"id":"https://openalex.org/C97489613","wikidata":"https://www.wikidata.org/wiki/Q842755","display_name":"Peano axioms","level":2,"score":0.17751330137252808},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1254948079586029}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.2307/421098","is_oa":false,"landing_page_url":"https://doi.org/10.2307/421098","pdf_url":null,"source":{"id":"https://openalex.org/S130801046","display_name":"Bulletin of Symbolic Logic","issn_l":"1079-8986","issn":["1079-8986","1943-5894"],"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":"Bulletin of Symbolic Logic","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.bsl/1182353535","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.bsl/1182353535","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:10.1.1.28.1539","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.28.1539","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.ucla.edu/~asl/bsl/0304/0304-001.ps","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.57.5485","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.57.5485","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.doc.ic.ac.uk/~ae/papers/survey.ps.Z","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":109,"referenced_works":["https://openalex.org/W75971611","https://openalex.org/W186368034","https://openalex.org/W207289571","https://openalex.org/W220096824","https://openalex.org/W286276113","https://openalex.org/W650925811","https://openalex.org/W1485844051","https://openalex.org/W1489200767","https://openalex.org/W1489704243","https://openalex.org/W1492711856","https://openalex.org/W1492775371","https://openalex.org/W1497475168","https://openalex.org/W1504035215","https://openalex.org/W1512478964","https://openalex.org/W1512502927","https://openalex.org/W1513445195","https://openalex.org/W1513576273","https://openalex.org/W1524305136","https://openalex.org/W1544564247","https://openalex.org/W1544662935","https://openalex.org/W1553231387","https://openalex.org/W1566092174","https://openalex.org/W1571138202","https://openalex.org/W1572053176","https://openalex.org/W1582269801","https://openalex.org/W1594563152","https://openalex.org/W1597097264","https://openalex.org/W1719974439","https://openalex.org/W1789681608","https://openalex.org/W1975444659","https://openalex.org/W1977525095","https://openalex.org/W1979684610","https://openalex.org/W1983705661","https://openalex.org/W1984190214","https://openalex.org/W1997422577","https://openalex.org/W1997766149","https://openalex.org/W1998538686","https://openalex.org/W2006368537","https://openalex.org/W2007270285","https://openalex.org/W2009183043","https://openalex.org/W2010839695","https://openalex.org/W2014744906","https://openalex.org/W2021020428","https://openalex.org/W2021433230","https://openalex.org/W2026278715","https://openalex.org/W2027362343","https://openalex.org/W2028924965","https://openalex.org/W2031900669","https://openalex.org/W2032386884","https://openalex.org/W2041876924","https://openalex.org/W2052324986","https://openalex.org/W2065250257","https://openalex.org/W2073030937","https://openalex.org/W2077752481","https://openalex.org/W2079735866","https://openalex.org/W2081395299","https://openalex.org/W2081739551","https://openalex.org/W2082241908","https://openalex.org/W2084041069","https://openalex.org/W2084743624","https://openalex.org/W2089617756","https://openalex.org/W2099482460","https://openalex.org/W2100612170","https://openalex.org/W2109523263","https://openalex.org/W2111963011","https://openalex.org/W2112361602","https://openalex.org/W2115154197","https://openalex.org/W2127112332","https://openalex.org/W2133225357","https://openalex.org/W2139772363","https://openalex.org/W2153333483","https://openalex.org/W2154273644","https://openalex.org/W2155748644","https://openalex.org/W2166644419","https://openalex.org/W2313585303","https://openalex.org/W2339378878","https://openalex.org/W2478145869","https://openalex.org/W2520815221","https://openalex.org/W2530006810","https://openalex.org/W2531442894","https://openalex.org/W2551720480","https://openalex.org/W2570480157","https://openalex.org/W2574937674","https://openalex.org/W2586374872","https://openalex.org/W2752853835","https://openalex.org/W2897302766","https://openalex.org/W2898851980","https://openalex.org/W2914212232","https://openalex.org/W3096424428","https://openalex.org/W3138265894","https://openalex.org/W3172363867","https://openalex.org/W4205579648","https://openalex.org/W4213381987","https://openalex.org/W4214637200","https://openalex.org/W4232709242","https://openalex.org/W4239316923","https://openalex.org/W4239497877","https://openalex.org/W4243711577","https://openalex.org/W4244540398","https://openalex.org/W4245757772","https://openalex.org/W4249775755","https://openalex.org/W4250696306","https://openalex.org/W4252813291","https://openalex.org/W4252846370","https://openalex.org/W4388310169","https://openalex.org/W4388310185","https://openalex.org/W6629500815","https://openalex.org/W6656922794","https://openalex.org/W6663985956"],"related_works":["https://openalex.org/W1665503308","https://openalex.org/W2325470895","https://openalex.org/W2378289559","https://openalex.org/W1681127796","https://openalex.org/W1967016391","https://openalex.org/W1968629980","https://openalex.org/W2374588602","https://openalex.org/W2349057364","https://openalex.org/W2080063910","https://openalex.org/W2000289880"],"abstract_inverted_index":{"Abstract":[0],"We":[1,121],"present":[2],"a":[3,50,62,96,111,123],"survey":[4],"of":[5,9,40,83,98,102,125,132],"the":[6,23,99,130],"recent":[7],"applications":[8,137],"continuous":[10],"domains":[11],"for":[12,17,114,127,157],"providing":[13],"simple":[14],"computational":[15,63],"models":[16,48],"classical":[18],"spaces":[19,37,39],"in":[20,65,68,129,138,142,161],"mathematics":[21,69],"including":[22],"real":[24,108,163],"line,":[25],"countably":[26],"based":[27],"locally":[28],"compact":[29],"spaces,":[30,34],"complete":[31],"separable":[32,35],"metric":[33],"Banach":[36],"and":[38,52,55,70,81,85,92,107,141],"probability":[41],"distributions.":[42],"It":[43],"is":[44],"shown":[45],"how":[46,56,151],"these":[47],"have":[49,88,154],"logical":[51],"effective":[53],"presentation":[54],"they":[57],"are":[58],"used":[59],"to":[60,146],"give":[61,122],"framework":[64],"several":[66],"areas":[67],"physics.":[71],"These":[72],"include":[73],"fractal":[74],"geometry,":[75],"where":[76,95,110],"new":[77],"results":[78],"on":[79],"existence":[80],"uniqueness":[82],"attractors":[84],"invariant":[86],"distributions":[87],"been":[89,105,119,155],"obtained,":[90],"measure":[91],"integration":[93,103],"theory,":[94],"generalization":[97],"Riemann":[100],"theory":[101,131],"has":[104,118],"developed,":[106],"arithmetic,":[109],"feasible":[112],"setting":[113],"exact":[115,162],"computer":[116],"arithmetic":[117],"formulated.":[120],"number":[124],"algorithms":[126,153],"computation":[128],"iterated":[133],"function":[134],"systems":[135],"with":[136],"statistical":[139],"physics":[140],"period":[143],"doubling":[144],"route":[145],"chaos;":[147],"we":[148],"also":[149],"show":[150],"efficient":[152],"obtained":[156],"computing":[158],"elementary":[159],"functions":[160],"arithmetic.":[164]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":7},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":6},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":6}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
