{"id":"https://openalex.org/W2162699259","doi":"https://doi.org/10.2307/2271897","title":"An algebraic characterization of power set in countable standard models of ZF","display_name":"An algebraic characterization of power set in countable standard models of ZF","publication_year":1975,"publication_date":"1975-06-01","ids":{"openalex":"https://openalex.org/W2162699259","doi":"https://doi.org/10.2307/2271897","mag":"2162699259"},"language":"en","primary_location":{"id":"doi:10.2307/2271897","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2271897","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/A5011700794","display_name":"G. Metakides","orcid":null},"institutions":[{"id":"https://openalex.org/I5388228","display_name":"University of Rochester","ror":"https://ror.org/022kthw22","country_code":"US","type":"education","lineage":["https://openalex.org/I5388228"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"George Metakides","raw_affiliation_strings":["University of Rochester, Rochester, New York 14627"],"affiliations":[{"raw_affiliation_string":"University of Rochester, Rochester, New York 14627","institution_ids":["https://openalex.org/I5388228"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5002637128","display_name":"J. M. Plotkin","orcid":null},"institutions":[{"id":"https://openalex.org/I87216513","display_name":"Michigan State University","ror":"https://ror.org/05hs6h993","country_code":"US","type":"education","lineage":["https://openalex.org/I87216513"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"J. M. Plotkin","raw_affiliation_strings":["Michigan State University, East Lansing, Michigan 48824"],"affiliations":[{"raw_affiliation_string":"Michigan State University, East Lansing, Michigan 48824","institution_ids":["https://openalex.org/I87216513"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5011700794"],"corresponding_institution_ids":["https://openalex.org/I5388228"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.14913194,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"40","issue":"2","first_page":"167","last_page":"170"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9775000214576721,"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":0.9775000214576721,"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/T10991","display_name":"Game Theory and Voting Systems","score":0.9718000292778015,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9714000225067139,"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/countable-set","display_name":"Countable set","score":0.8271962404251099},{"id":"https://openalex.org/keywords/two-element-boolean-algebra","display_name":"Two-element Boolean algebra","score":0.8135160803794861},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8112097978591919},{"id":"https://openalex.org/keywords/complete-boolean-algebra","display_name":"Complete Boolean algebra","score":0.8086467981338501},{"id":"https://openalex.org/keywords/boolean-algebra","display_name":"Boolean algebra","score":0.6698080897331238},{"id":"https://openalex.org/keywords/free-boolean-algebra","display_name":"Free Boolean algebra","score":0.6535962224006653},{"id":"https://openalex.org/keywords/boolean-algebras-canonically-defined","display_name":"Boolean algebras canonically defined","score":0.6262766122817993},{"id":"https://openalex.org/keywords/stones-representation-theorem-for-boolean-algebras","display_name":"Stone's representation theorem for Boolean algebras","score":0.6163142919540405},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5676524639129639},{"id":"https://openalex.org/keywords/power-set","display_name":"Power set","score":0.5396331548690796},{"id":"https://openalex.org/keywords/axiom","display_name":"Axiom","score":0.4520280063152313},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.40347230434417725},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.3625183701515198},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.336914598941803},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.25443097949028015},{"id":"https://openalex.org/keywords/algebra-representation","display_name":"Algebra representation","score":0.1908518671989441}],"concepts":[{"id":"https://openalex.org/C110729354","wikidata":"https://www.wikidata.org/wiki/Q185478","display_name":"Countable set","level":2,"score":0.8271962404251099},{"id":"https://openalex.org/C207764348","wikidata":"https://www.wikidata.org/wiki/Q7858706","display_name":"Two-element Boolean algebra","level":4,"score":0.8135160803794861},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8112097978591919},{"id":"https://openalex.org/C81518389","wikidata":"https://www.wikidata.org/wiki/Q5156447","display_name":"Complete Boolean algebra","level":5,"score":0.8086467981338501},{"id":"https://openalex.org/C39685927","wikidata":"https://www.wikidata.org/wiki/Q173183","display_name":"Boolean algebra","level":2,"score":0.6698080897331238},{"id":"https://openalex.org/C188159880","wikidata":"https://www.wikidata.org/wiki/Q5499761","display_name":"Free Boolean algebra","level":5,"score":0.6535962224006653},{"id":"https://openalex.org/C45503250","wikidata":"https://www.wikidata.org/wiki/Q4943350","display_name":"Boolean algebras canonically defined","level":5,"score":0.6262766122817993},{"id":"https://openalex.org/C10021369","wikidata":"https://www.wikidata.org/wiki/Q1166774","display_name":"Stone's representation theorem for Boolean algebras","level":5,"score":0.6163142919540405},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5676524639129639},{"id":"https://openalex.org/C100643331","wikidata":"https://www.wikidata.org/wiki/Q205170","display_name":"Power set","level":3,"score":0.5396331548690796},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.4520280063152313},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.40347230434417725},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.3625183701515198},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.336914598941803},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.25443097949028015},{"id":"https://openalex.org/C14394260","wikidata":"https://www.wikidata.org/wiki/Q4723980","display_name":"Algebra representation","level":3,"score":0.1908518671989441},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.2307/2271897","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2271897","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/1183739378","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1183739378","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":3,"referenced_works":["https://openalex.org/W655855359","https://openalex.org/W1545797722","https://openalex.org/W4291439952"],"related_works":["https://openalex.org/W2940617399","https://openalex.org/W4256012180","https://openalex.org/W2037090414","https://openalex.org/W2369221237","https://openalex.org/W2064028328","https://openalex.org/W4243109641","https://openalex.org/W2043703128","https://openalex.org/W2077969106","https://openalex.org/W3211128338","https://openalex.org/W2516433860"],"abstract_inverted_index":{"The":[0],"following":[1],"is":[2,13,33,41,59,87,128,187,193,210,216],"a":[3,16,34,42,49,60,68,188,194,202,213],"classical":[4],"result:":[5],"Theorem":[6],"1.1.":[7,180],"A":[8,181],"complete":[9,50],"atomic":[10],"Boolean":[11,75,147,166,183],"algebra":[12,19,76,93,148,184],"isomorphic":[14,88,141],"to":[15,89,142],"power":[17,91,172],"set":[18,92,190,203,215],"[2,":[20],"p":[21],".":[22,98,157],"70].":[23],"One":[24],"of":[25,28,38,48,65,77,86,94,106,114,149,155,177,198],"the":[26,74,90,104,112,143,150,159],"consequences":[27],"[3]":[29],"is:":[30],"If":[31],"M":[32,45],"countable":[35,43,61,182,195],"standard":[36,62,175,196],"model":[37,47,63,197],"ZF":[39,66],"and":[40,67,102,131,152,201],"(in":[44,79],")":[46,84],"\u2135":[51],"0":[52],"-categorical":[53],"theory":[54,105],"T":[55,80,103],",":[56,125],"then":[57,126],"there":[58,127,192],"N":[64,71,97,130,134,138,200,206],"\u039b":[69,95,132,204],"\u2208":[70,133,205],"such":[72,207],"that":[73,163,208,212],"definable":[78],"with":[81,108,135],"parameters":[82],"from":[83],"subsets":[85,154],"in":[96,174],"In":[99],"particular":[100],"if":[101,191],"equality":[107],"additional":[109],"axioms":[110],"asserting":[111],"existence":[113],"at":[115],"least":[116],"n":[117,122],"distinct":[118],"elements":[119],"for":[120],"each":[121],"&lt;":[123],"\u03c9":[124,156],"an":[129],"\u3008":[136],"P":[137],"(\u039b),":[139],"\u2286\u3009":[140],"countable,":[144],"atomic,":[145],"incomplete":[146,165],"finite":[151],"cofinite":[153],"From":[158],"above":[160],"we":[161],"see":[162],"some":[164],"algebras":[167],"can":[168],"be":[169],"realized":[170],"as":[171],"sets":[173],"models":[176],"ZF.":[178],"Definition":[179],"\u3008B,":[185],"\u2264\u3009":[186],"pseudo-power":[189,214],"ZF,":[199],"It":[209],"clear":[211],"atomic.":[217]},"counts_by_year":[],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
