{"id":"https://openalex.org/W2096250827","doi":"https://doi.org/10.1017/s0022481200051380","title":"Derived rules of inference related to the continuity of effective operations","display_name":"Derived rules of inference related to the continuity of effective operations","publication_year":1976,"publication_date":"1976-06-01","ids":{"openalex":"https://openalex.org/W2096250827","doi":"https://doi.org/10.1017/s0022481200051380","mag":"2096250827"},"language":"en","primary_location":{"id":"doi:10.1017/s0022481200051380","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0022481200051380","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/A5034098863","display_name":"Michael Beeson","orcid":"https://orcid.org/0000-0001-9259-1220"},"institutions":[{"id":"https://openalex.org/I86519309","display_name":"The University of Texas at Austin","ror":"https://ror.org/00hj54h04","country_code":"US","type":"education","lineage":["https://openalex.org/I86519309"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Michael J. Beeson","raw_affiliation_strings":["University of Texas, Austin, Texas 78712"],"affiliations":[{"raw_affiliation_string":"University of Texas, Austin, Texas 78712","institution_ids":["https://openalex.org/I86519309"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5034098863"],"corresponding_institution_ids":["https://openalex.org/I86519309"],"apc_list":null,"apc_paid":null,"fwci":2.8706,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.92166305,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":null,"biblio":{"volume":"41","issue":"2","first_page":"328","last_page":"336"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9957000017166138,"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":0.9957000017166138,"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":0.9934999942779541,"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":0.9923999905586243,"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/closure","display_name":"Closure (psychology)","score":0.7369317412376404},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.6977776885032654},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6955608129501343},{"id":"https://openalex.org/keywords/constructive","display_name":"Constructive","score":0.6621319651603699},{"id":"https://openalex.org/keywords/rule-of-inference","display_name":"Rule of inference","score":0.5035020709037781},{"id":"https://openalex.org/keywords/inference","display_name":"Inference","score":0.4758034646511078},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.4229316711425781},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4148217737674713},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3941560983657837},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.36508941650390625},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2892032861709595},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.10351049900054932},{"id":"https://openalex.org/keywords/process","display_name":"Process (computing)","score":0.07119375467300415},{"id":"https://openalex.org/keywords/law","display_name":"Law","score":0.07045045495033264}],"concepts":[{"id":"https://openalex.org/C146834321","wikidata":"https://www.wikidata.org/wiki/Q2979672","display_name":"Closure (psychology)","level":2,"score":0.7369317412376404},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.6977776885032654},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6955608129501343},{"id":"https://openalex.org/C2778701210","wikidata":"https://www.wikidata.org/wiki/Q28130034","display_name":"Constructive","level":3,"score":0.6621319651603699},{"id":"https://openalex.org/C3746660","wikidata":"https://www.wikidata.org/wiki/Q1068763","display_name":"Rule of inference","level":2,"score":0.5035020709037781},{"id":"https://openalex.org/C2776214188","wikidata":"https://www.wikidata.org/wiki/Q408386","display_name":"Inference","level":2,"score":0.4758034646511078},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.4229316711425781},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4148217737674713},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3941560983657837},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.36508941650390625},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2892032861709595},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.10351049900054932},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.07119375467300415},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.07045045495033264},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1017/s0022481200051380","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0022481200051380","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/1183739773","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1183739773","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":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W1608607427","https://openalex.org/W1854750410","https://openalex.org/W1986581424","https://openalex.org/W2067914884","https://openalex.org/W2127553594","https://openalex.org/W2256089923","https://openalex.org/W2744169538","https://openalex.org/W3046397786"],"related_works":["https://openalex.org/W2959217929","https://openalex.org/W4242866892","https://openalex.org/W84644661","https://openalex.org/W42551271","https://openalex.org/W2040777999","https://openalex.org/W3203330043","https://openalex.org/W1584374742","https://openalex.org/W2119264717","https://openalex.org/W102683223","https://openalex.org/W2710049634"],"abstract_inverted_index":{"In":[0,69,188],"[B1]":[1],"and":[2,133,153,165,168,196,224],"[B2]":[3,190],"we":[4,71],"have":[5,45],"shown":[6,193],"that":[7,33,194,216,225],"the":[8,12,39,46,79,179,213,259],"classical":[9,214],"theorems":[10,233],"on":[11,130,137,178],"continuity":[13,105,141],"of":[14,27,42,78,104,124,145,185,212,258],"effective":[15,59,89,125,176],"operations":[16,129,136,144,177],"are":[17,36,184,198,227],"not":[18,219,228],"derivable":[19,199,229],"in":[20,200,222,230,250],"various":[21,241],"constructive":[22],"formal":[23],"systems.":[24],"The":[25,140,244],"purpose":[26],"this":[28,251],"paper":[29,252],"is":[30,112,148,154,160,169,192,238],"to":[31,53,66,86,97,150,162,247,261],"establish":[32,72],"these":[34],"systems":[35,260],"closed":[37],"under":[38,74],"corresponding":[40],"rules":[41,77,246],"inference,":[43],"which":[44,183,262],"form:":[47],"If":[48],"e":[49,62,82,92,107,110,116],"can":[50,63,83,94],"be":[51,54,64,67,84,87,95,98,248],"proved":[52,65,85,96],"(the":[55,99],"index":[56,100],"of)":[57,101],"an":[58,88],"operation,":[60,90],"then":[61,91],"continuous.":[68],"fact":[70],"closure":[73,256],"apparently":[75],"stronger":[76,242],"form,":[80],"if":[81],"*":[93,111],"a":[102],"modulus":[103],"for":[106,143,157],",":[108],"where":[109],"canonically":[113],"obtained":[114],"from":[115,204,210],".":[117],"We":[118,172],"again":[119],"deal":[120,174],"with":[121,175],"two":[122],"kinds":[123],"operations:":[126],"(i)":[127,147],"partial":[128,131],"arguments,":[132],"(ii)":[134,159],"total":[135,138],"arguments.":[139],"theorem":[142],"kind":[146,158,186],"due":[149,161],"Myhill-Shepherdson":[151],"[MS]":[152],"called":[155,170],"MS;":[156],"Kreisel,":[163],"Lacombe,":[164],"Shoenfield":[166],"[KLS]":[167],"KLS.":[171],"also":[173],"(recursive)":[180],"real":[181],"numbers,":[182],"(ii).":[187],"[B1],":[189],"it":[191],"KLS":[195],"MS":[197],"in-tuitionistic":[201],"arithmetic":[202],"HA":[203,237],"Markov's":[205],"principle":[206],"MP":[207,221],"(this":[208],"follows":[209],"examination":[211],"proofs);":[215],"they":[217,226,263],"do":[218],"imply":[220],"HA;":[223],"HA.":[231],"(These":[232],"remain":[234],"true":[235],"when":[236],"replaced":[239],"by":[240],"systems.)":[243],"derived":[245],"established":[249],"therefore":[253],"represent":[254],"nontrivial":[255],"properties":[257],"apply.":[264]},"counts_by_year":[],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}