{"id":"https://openalex.org/W2782806128","doi":"https://doi.org/10.23638/lmcs-14(4:1)2018","title":"Applicable Mathematics in a Minimal Computational Theory of Sets","display_name":"Applicable Mathematics in a Minimal Computational Theory of Sets","publication_year":2018,"publication_date":"2018-10-16","ids":{"openalex":"https://openalex.org/W2782806128","doi":"https://doi.org/10.23638/lmcs-14(4:1)2018","mag":"2782806128"},"language":"en","primary_location":{"id":"doi:10.23638/lmcs-14(4:1)2018","is_oa":true,"landing_page_url":"https://doi.org/10.23638/lmcs-14(4:1)2018","pdf_url":"https://lmcs.episciences.org/4891/pdf","source":{"id":"https://openalex.org/S114379355","display_name":"Logical Methods in Computer Science","issn_l":"1860-5974","issn":["1860-5974"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313916","host_organization_name":"Logical Methods in Computer Science e.V.","host_organization_lineage":["https://openalex.org/P4310313916"],"host_organization_lineage_names":["Logical Methods in Computer Science e.V."],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Logical Methods in Computer Science","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://lmcs.episciences.org/4891/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5071426595","display_name":"Arnon Avron","orcid":"https://orcid.org/0000-0001-6831-3343"},"institutions":[{"id":"https://openalex.org/I16391192","display_name":"Tel Aviv University","ror":"https://ror.org/04mhzgx49","country_code":"IL","type":"education","lineage":["https://openalex.org/I16391192"]},{"id":"https://openalex.org/I205783295","display_name":"Cornell University","ror":"https://ror.org/05bnh6r87","country_code":"US","type":"education","lineage":["https://openalex.org/I205783295"]}],"countries":["IL","US"],"is_corresponding":false,"raw_author_name":"Arnon Avron","raw_affiliation_strings":["Cornell University , Ithaca , NY , USA","Tel Aviv University , Tel-Aviv , Israel"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Cornell University , Ithaca , NY , USA","institution_ids":["https://openalex.org/I205783295"]},{"raw_affiliation_string":"Tel Aviv University , Tel-Aviv , Israel","institution_ids":["https://openalex.org/I16391192"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5029629129","display_name":"Liron Cohen","orcid":"https://orcid.org/0000-0002-6608-3000"},"institutions":[{"id":"https://openalex.org/I16391192","display_name":"Tel Aviv University","ror":"https://ror.org/04mhzgx49","country_code":"IL","type":"education","lineage":["https://openalex.org/I16391192"]},{"id":"https://openalex.org/I205783295","display_name":"Cornell University","ror":"https://ror.org/05bnh6r87","country_code":"US","type":"education","lineage":["https://openalex.org/I205783295"]}],"countries":["IL","US"],"is_corresponding":false,"raw_author_name":"Liron Cohen","raw_affiliation_strings":["Cornell University , Ithaca , NY , USA","Tel Aviv University , Tel-Aviv , Israel"],"raw_orcid":"https://orcid.org/0000-0002-6608-3000","affiliations":[{"raw_affiliation_string":"Cornell University , Ithaca , NY , USA","institution_ids":["https://openalex.org/I205783295"]},{"raw_affiliation_string":"Tel Aviv University , Tel-Aviv , Israel","institution_ids":["https://openalex.org/I16391192"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.01380005,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"Volume 14, Issue 4","issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9987999796867371,"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":0.9987999796867371,"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/T11151","display_name":"Advanced Topology and Set Theory","score":0.9976999759674072,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.9972000122070312,"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/unary-operation","display_name":"Unary operation","score":0.7396617531776428},{"id":"https://openalex.org/keywords/predicate","display_name":"Predicate (mathematical logic)","score":0.7018780708312988},{"id":"https://openalex.org/keywords/transitive-relation","display_name":"Transitive relation","score":0.5938301086425781},{"id":"https://openalex.org/keywords/hierarchy","display_name":"Hierarchy","score":0.5341562032699585},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5135052800178528},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.4987337589263916},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.47384077310562134},{"id":"https://openalex.org/keywords/set-theory","display_name":"Set theory","score":0.47216007113456726},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.4567992687225342},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.45089036226272583},{"id":"https://openalex.org/keywords/morphism","display_name":"Morphism","score":0.4405827820301056},{"id":"https://openalex.org/keywords/conservative-extension","display_name":"Conservative extension","score":0.4201295077800751},{"id":"https://openalex.org/keywords/logical-framework","display_name":"Logical framework","score":0.4112505614757538},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.36965256929397583},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.3659270107746124},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.36447668075561523},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3573550581932068},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.20921429991722107},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1469244658946991},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.12194347381591797},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.10268744826316833}],"concepts":[{"id":"https://openalex.org/C78023250","wikidata":"https://www.wikidata.org/wiki/Q657596","display_name":"Unary operation","level":2,"score":0.7396617531776428},{"id":"https://openalex.org/C140146324","wikidata":"https://www.wikidata.org/wiki/Q1144319","display_name":"Predicate (mathematical logic)","level":2,"score":0.7018780708312988},{"id":"https://openalex.org/C191399111","wikidata":"https://www.wikidata.org/wiki/Q64861","display_name":"Transitive relation","level":2,"score":0.5938301086425781},{"id":"https://openalex.org/C31170391","wikidata":"https://www.wikidata.org/wiki/Q188619","display_name":"Hierarchy","level":2,"score":0.5341562032699585},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5135052800178528},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.4987337589263916},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.47384077310562134},{"id":"https://openalex.org/C153046414","wikidata":"https://www.wikidata.org/wiki/Q12482","display_name":"Set theory","level":3,"score":0.47216007113456726},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4567992687225342},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.45089036226272583},{"id":"https://openalex.org/C137212723","wikidata":"https://www.wikidata.org/wiki/Q1948412","display_name":"Morphism","level":2,"score":0.4405827820301056},{"id":"https://openalex.org/C2780432614","wikidata":"https://www.wikidata.org/wiki/Q864213","display_name":"Conservative extension","level":2,"score":0.4201295077800751},{"id":"https://openalex.org/C20693621","wikidata":"https://www.wikidata.org/wiki/Q6667502","display_name":"Logical framework","level":2,"score":0.4112505614757538},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.36965256929397583},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3659270107746124},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.36447668075561523},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3573550581932068},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.20921429991722107},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1469244658946991},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.12194347381591797},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.10268744826316833},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","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/C34447519","wikidata":"https://www.wikidata.org/wiki/Q179522","display_name":"Market economy","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.23638/lmcs-14(4:1)2018","is_oa":true,"landing_page_url":"https://doi.org/10.23638/lmcs-14(4:1)2018","pdf_url":"https://lmcs.episciences.org/4891/pdf","source":{"id":"https://openalex.org/S114379355","display_name":"Logical Methods in Computer Science","issn_l":"1860-5974","issn":["1860-5974"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313916","host_organization_name":"Logical Methods in Computer Science e.V.","host_organization_lineage":["https://openalex.org/P4310313916"],"host_organization_lineage_names":["Logical Methods in Computer Science e.V."],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Logical Methods in Computer Science","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1801.02387","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1801.02387","pdf_url":"https://arxiv.org/pdf/1801.02387","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"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":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.1801.02387","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1801.02387","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"},{"id":"mag:2963870399","is_oa":true,"landing_page_url":"http://arxiv.org/pdf/1801.02387.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":"arXiv (Cornell University)","raw_type":null}],"best_oa_location":{"id":"doi:10.23638/lmcs-14(4:1)2018","is_oa":true,"landing_page_url":"https://doi.org/10.23638/lmcs-14(4:1)2018","pdf_url":"https://lmcs.episciences.org/4891/pdf","source":{"id":"https://openalex.org/S114379355","display_name":"Logical Methods in Computer Science","issn_l":"1860-5974","issn":["1860-5974"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313916","host_organization_name":"Logical Methods in Computer Science e.V.","host_organization_lineage":["https://openalex.org/P4310313916"],"host_organization_lineage_names":["Logical Methods in Computer Science e.V."],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Logical Methods in Computer Science","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320320946","display_name":"Weizmann Institute of Science","ror":"https://ror.org/0316ej306"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2782806128.pdf","grobid_xml":"https://content.openalex.org/works/W2782806128.grobid-xml"},"referenced_works_count":23,"referenced_works":["https://openalex.org/W67269200","https://openalex.org/W1487202929","https://openalex.org/W1491173026","https://openalex.org/W1585022015","https://openalex.org/W1823991804","https://openalex.org/W1971165519","https://openalex.org/W2010273585","https://openalex.org/W2024315465","https://openalex.org/W2041273376","https://openalex.org/W2049069313","https://openalex.org/W2057062089","https://openalex.org/W2066527932","https://openalex.org/W2070231112","https://openalex.org/W2078719364","https://openalex.org/W2081002360","https://openalex.org/W2092169546","https://openalex.org/W2106192381","https://openalex.org/W2128057448","https://openalex.org/W2129133014","https://openalex.org/W2135443831","https://openalex.org/W2142694326","https://openalex.org/W2158593143","https://openalex.org/W2798922842"],"related_works":["https://openalex.org/W1617384822","https://openalex.org/W2898891135","https://openalex.org/W2809176260","https://openalex.org/W1551622500","https://openalex.org/W2019447115","https://openalex.org/W2521846953","https://openalex.org/W49443643","https://openalex.org/W2478383650","https://openalex.org/W1840071381","https://openalex.org/W1889411575"],"abstract_inverted_index":{"In":[0,35],"previous":[1],"papers":[2],"on":[3,66],"this":[4,36,141],"project":[5],"a":[6,103,166,171],"general":[7],"static":[8,58,183],"logical":[9],"framework":[10,32,42,79],"for":[11,48,145],"formalizing":[12],"and":[13,22],"mechanizing":[14],"set":[15],"theories":[16,29],"of":[17,25,63,82,94,112,121,153,162,191],"different":[18],"strength":[19],"was":[20,33],"suggested,":[21],"the":[23,64,77,80,83,92,107,130,160,179,182,188,192],"power":[24,81],"some":[26,120],"predicatively":[27],"acceptable":[28],"in":[30,88,106,133,178,187],"that":[31,41,90,99,100,109,139,169],"explored.":[34],"work":[37],"we":[38,72,137],"first":[39,189],"improve":[40],"by":[43,51,119,181],"enriching":[44],"it":[45,68,89],"with":[46],"means":[47],"coherently":[49],"extending":[50],"definitions":[52],"its":[53,57,113,122],"theories,":[54],"without":[55],"destroying":[56],"nature":[59],"or":[60],"violating":[61],"any":[62],"principles":[65],"which":[67,174],"is":[69,102,117],"based.":[70],"Then":[71,136],"turn":[73],"to":[74,128],"investigate":[75],"within":[76],"enriched":[78],"minimal":[84,114,142],"(predicatively":[85],"acceptable)":[86],"theory":[87,101,143,180],"proves":[91],"existence":[93],"infinite":[95],"sets.":[96],"We":[97],"show":[98,138],"computational":[104],"theory,":[105],"sense":[108],"every":[110],"element":[111],"transitive":[115],"model":[116,126],"denoted":[118],"closed":[123],"terms.":[124],"(That":[125],"happens":[127],"be":[129,176],"second":[131],"universe":[132],"Jensen's":[134],"hierarchy.)":[135],"already":[140],"suffices":[144],"developing":[146],"very":[147],"large":[148],"portions":[149],"(if":[150],"not":[151],"all)":[152],"scientifically":[154],"applicable":[155],"mathematics.":[156],"This":[157],"requires":[158],"treating":[159],"collection":[161],"real":[163],"numbers":[164],"as":[165],"proper":[167],"class,":[168],"is:":[170],"unary":[172],"predicate":[173],"can":[175],"introduced":[177],"extension":[184],"method":[185],"described":[186],"part":[190],"paper.":[193]},"counts_by_year":[{"year":2024,"cited_by_count":1}],"updated_date":"2026-08-05T07:39:15.569665","created_date":"2025-10-10T00:00:00"}
