{"id":"https://openalex.org/W2166541776","doi":"https://doi.org/10.2307/2273098","title":"Real-valued models with metric equality and uniformly continuous predicates","display_name":"Real-valued models with metric equality and uniformly continuous predicates","publication_year":1982,"publication_date":"1982-12-01","ids":{"openalex":"https://openalex.org/W2166541776","doi":"https://doi.org/10.2307/2273098","mag":"2166541776"},"language":"en","primary_location":{"id":"doi:10.2307/2273098","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2273098","pdf_url":null,"source":{"id":"https://openalex.org/S177675236","display_name":"Journal of Symbolic Logic","issn_l":"0022-4812","issn":["0022-4812","1943-5886"],"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":"Journal 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/A5085273561","display_name":"Michael Katz","orcid":"https://orcid.org/0000-0002-6238-376X"},"institutions":[{"id":"https://openalex.org/I204722609","display_name":"Queen's University","ror":"https://ror.org/02y72wh86","country_code":"CA","type":"education","lineage":["https://openalex.org/I204722609"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Michael Katz","raw_affiliation_strings":["Departement of Mathematics and Statistics, Queen's University, Kingston, Ontario, Canada"],"affiliations":[{"raw_affiliation_string":"Departement of Mathematics and Statistics, Queen's University, Kingston, Ontario, Canada","institution_ids":["https://openalex.org/I204722609"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5085273561"],"corresponding_institution_ids":["https://openalex.org/I204722609"],"apc_list":null,"apc_paid":null,"fwci":6.9114,"has_fulltext":false,"cited_by_count":18,"citation_normalized_percentile":{"value":0.96535297,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"47","issue":"4","first_page":"772","last_page":"792"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9991000294685364,"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"}},"topics":[{"id":"https://openalex.org/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9991000294685364,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.9975000023841858,"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":0.9857000112533569,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.7003663182258606},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6758617162704468},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.6681246757507324},{"id":"https://openalex.org/keywords/metric-space","display_name":"Metric space","score":0.5481902360916138},{"id":"https://openalex.org/keywords/rule-of-inference","display_name":"Rule of inference","score":0.4566660225391388},{"id":"https://openalex.org/keywords/inference","display_name":"Inference","score":0.4492076337337494},{"id":"https://openalex.org/keywords/real-number","display_name":"Real number","score":0.433453768491745},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4294389486312866},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.41875308752059937},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3732016682624817},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.25310343503952026},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1736629605293274},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.054825931787490845}],"concepts":[{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.7003663182258606},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6758617162704468},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.6681246757507324},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.5481902360916138},{"id":"https://openalex.org/C3746660","wikidata":"https://www.wikidata.org/wiki/Q1068763","display_name":"Rule of inference","level":2,"score":0.4566660225391388},{"id":"https://openalex.org/C2776214188","wikidata":"https://www.wikidata.org/wiki/Q408386","display_name":"Inference","level":2,"score":0.4492076337337494},{"id":"https://openalex.org/C94020503","wikidata":"https://www.wikidata.org/wiki/Q12916","display_name":"Real number","level":2,"score":0.433453768491745},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4294389486312866},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.41875308752059937},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3732016682624817},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.25310343503952026},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1736629605293274},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.054825931787490845},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.2307/2273098","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2273098","pdf_url":null,"source":{"id":"https://openalex.org/S177675236","display_name":"Journal of Symbolic Logic","issn_l":"0022-4812","issn":["0022-4812","1943-5886"],"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":"Journal of Symbolic Logic","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.jsl/1183741138","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1183741138","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"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","score":0.699999988079071,"display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W1661259631","https://openalex.org/W1980180357","https://openalex.org/W1994831517","https://openalex.org/W2010765987","https://openalex.org/W2035553573","https://openalex.org/W2062692391","https://openalex.org/W2080126541","https://openalex.org/W2092180595","https://openalex.org/W2170862108","https://openalex.org/W4250045393","https://openalex.org/W6645391091","https://openalex.org/W6666108427"],"related_works":["https://openalex.org/W3203330043","https://openalex.org/W4297851895","https://openalex.org/W1584374742","https://openalex.org/W2119264717","https://openalex.org/W102683223","https://openalex.org/W2710049634","https://openalex.org/W2047356095","https://openalex.org/W1984225148","https://openalex.org/W1559068841","https://openalex.org/W2547621624"],"abstract_inverted_index":{"Abstract":[0],"Two":[1],"real-valued":[2,33],"deduction":[3],"schemes":[4],"are":[5,22],"introduced,":[6],"which":[7],"agree":[8],"on":[9,14,40],"\u22a2":[10,16,21],"\u22bf":[11],"but":[12],"not":[13],"\u0393":[15,19],"\u22bf,":[17],"where":[18],"and":[20,79,99],"finite":[23],"sets":[24],"of":[25,43,54,65,67,88,102,104,108],"formulae.":[26],"Using":[27],"the":[28,41,48,62,80,96,109],"first":[29],"scheme":[30,50],"we":[31],"axiomatize":[32],"equality":[34],"so":[35],"that":[36],"it":[37],"induces":[38],"metrics":[39],"domains":[42],"appropriate":[44,81],"structures.":[45,70],"We":[46,91],"use":[47],"second":[49],"to":[51,56,61,76],"reduce":[52],"substitutivity":[53],"equals":[55],"uniform":[57],"continuity,":[58],"with":[59],"respect":[60],"metric":[63,89],"equality,":[64],"interpretations":[66],"predicates":[68,75],"in":[69],"This":[71],"continuity":[72],"extends":[73],"from":[74],"arbitrary":[77],"formulae":[78],"models":[82],"have":[83],"completions":[84,87],"resembling":[85],"analytic":[86],"spaces.":[90],"provide":[92],"inference":[93],"rules":[94],"for":[95],"two":[97],"deductions":[98],"discuss":[100],"definability":[101],"each":[103],"them":[105],"by":[106],"means":[107],"other.":[110]},"counts_by_year":[{"year":2017,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}