{"id":"https://openalex.org/W2062319438","doi":"https://doi.org/10.2178/bsl/1231081369","title":"A Brief Introduction to Algebraic Set Theory","display_name":"A Brief Introduction to Algebraic Set Theory","publication_year":2008,"publication_date":"2008-09-01","ids":{"openalex":"https://openalex.org/W2062319438","doi":"https://doi.org/10.2178/bsl/1231081369","mag":"2062319438"},"language":"en","primary_location":{"id":"doi:10.2178/bsl/1231081369","is_oa":true,"landing_page_url":"https://doi.org/10.2178/bsl/1231081369","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/4BD5763B1DCEED817B7C68AB7107483A/S107989860000158Xa.pdf/div-class-title-a-brief-introduction-to-algebraic-set-theory-div.pdf","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","datacite"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/4BD5763B1DCEED817B7C68AB7107483A/S107989860000158Xa.pdf/div-class-title-a-brief-introduction-to-algebraic-set-theory-div.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5048294977","display_name":"Steve Awodey","orcid":"https://orcid.org/0000-0001-9005-179X"},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Steve Awodey","raw_affiliation_strings":["Department of Philosophy, Carnegie Mellon University, Pittsburgh, PA 15213, USAE-mail:","Carnegie Mellon University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Philosophy, Carnegie Mellon University, Pittsburgh, PA 15213, USAE-mail:","institution_ids":["https://openalex.org/I74973139"]},{"raw_affiliation_string":"Carnegie Mellon University","institution_ids":["https://openalex.org/I74973139"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5048294977"],"corresponding_institution_ids":["https://openalex.org/I74973139"],"apc_list":null,"apc_paid":null,"fwci":5.3756,"has_fulltext":true,"cited_by_count":15,"citation_normalized_percentile":{"value":0.95094426,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":"14","issue":"3","first_page":"281","last_page":"298"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9977999925613403,"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/T10126","display_name":"Logic, programming, and type systems","score":0.9977999925613403,"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/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9965999722480774,"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/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.9955000281333923,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/realizability","display_name":"Realizability","score":0.8314847350120544},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6466450095176697},{"id":"https://openalex.org/keywords/topos-theory","display_name":"Topos theory","score":0.583712100982666},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.5631400942802429},{"id":"https://openalex.org/keywords/set-theory","display_name":"Set theory","score":0.5595504641532898},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.5252913236618042},{"id":"https://openalex.org/keywords/sheaf","display_name":"Sheaf","score":0.5069044232368469},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4930588901042938},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.44181811809539795},{"id":"https://openalex.org/keywords/real-algebraic-geometry","display_name":"Real algebraic geometry","score":0.4314414858818054},{"id":"https://openalex.org/keywords/constructive","display_name":"Constructive","score":0.429824560880661},{"id":"https://openalex.org/keywords/variety","display_name":"Variety (cybernetics)","score":0.4226023554801941},{"id":"https://openalex.org/keywords/unification","display_name":"Unification","score":0.4205821752548218},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.4171212315559387},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.35057467222213745},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.31726905703544617},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2602640390396118},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.16776716709136963}],"concepts":[{"id":"https://openalex.org/C2776378722","wikidata":"https://www.wikidata.org/wiki/Q3454417","display_name":"Realizability","level":2,"score":0.8314847350120544},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6466450095176697},{"id":"https://openalex.org/C182141236","wikidata":"https://www.wikidata.org/wiki/Q2143621","display_name":"Topos theory","level":2,"score":0.583712100982666},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5631400942802429},{"id":"https://openalex.org/C153046414","wikidata":"https://www.wikidata.org/wiki/Q12482","display_name":"Set theory","level":3,"score":0.5595504641532898},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.5252913236618042},{"id":"https://openalex.org/C4017995","wikidata":"https://www.wikidata.org/wiki/Q595298","display_name":"Sheaf","level":2,"score":0.5069044232368469},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4930588901042938},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.44181811809539795},{"id":"https://openalex.org/C2731732","wikidata":"https://www.wikidata.org/wiki/Q7301119","display_name":"Real algebraic geometry","level":3,"score":0.4314414858818054},{"id":"https://openalex.org/C2778701210","wikidata":"https://www.wikidata.org/wiki/Q28130034","display_name":"Constructive","level":3,"score":0.429824560880661},{"id":"https://openalex.org/C136197465","wikidata":"https://www.wikidata.org/wiki/Q1729295","display_name":"Variety (cybernetics)","level":2,"score":0.4226023554801941},{"id":"https://openalex.org/C96146094","wikidata":"https://www.wikidata.org/wiki/Q609057","display_name":"Unification","level":2,"score":0.4205821752548218},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.4171212315559387},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.35057467222213745},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.31726905703544617},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2602640390396118},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.16776716709136963},{"id":"https://openalex.org/C124952713","wikidata":"https://www.wikidata.org/wiki/Q8242","display_name":"Literature","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},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","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},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.0}],"mesh":[],"locations_count":11,"locations":[{"id":"doi:10.2178/bsl/1231081369","is_oa":true,"landing_page_url":"https://doi.org/10.2178/bsl/1231081369","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/4BD5763B1DCEED817B7C68AB7107483A/S107989860000158Xa.pdf/div-class-title-a-brief-introduction-to-algebraic-set-theory-div.pdf","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:repository.cmu.edu:philosophy-1065","is_oa":false,"landing_page_url":"http://repository.cmu.edu/cgi/viewcontent.cgi?article=1065&context=philosophy","pdf_url":null,"source":{"id":"https://openalex.org/S7407050927","display_name":"KiltHub Repository","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Department of Philosophy","raw_type":"text"},{"id":"pmh:doi:10.1184/r1/6490682","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":"Journal contribution"},{"id":"pmh:oai:CULeuclid:euclid.bsl/1231081369","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.bsl/1231081369","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:10.1.1.145.7202","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.145.7202","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.andrew.cmu.edu/user/awodey/japan/ast.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.154.6416","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.154.6416","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.andrew.cmu.edu/~awodey/preprints/astIntroFinal.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.359.4179","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.359.4179","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.421.3259","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.421.3259","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.andrew.cmu.edu/user/awodey/preprints/astIntro.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.931.3491","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.931.3491","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://repository.cmu.edu/cgi/viewcontent.cgi?article%3D1065%26context%3Dphilosophy","raw_type":"text"},{"id":"pmh:oai:figshare.com:article/6490682","is_oa":true,"landing_page_url":"https://figshare.com/articles/journal_contribution/A_Brief_Introduction_to_Algebraic_Set_Theory/6490682","pdf_url":null,"source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"doi:10.1184/r1/6490682.v1","is_oa":true,"landing_page_url":"https://doi.org/10.1184/r1/6490682.v1","pdf_url":null,"source":{"id":"https://openalex.org/S7407050927","display_name":"KiltHub Repository","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"JournalArticle"}],"best_oa_location":{"id":"doi:10.2178/bsl/1231081369","is_oa":true,"landing_page_url":"https://doi.org/10.2178/bsl/1231081369","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/4BD5763B1DCEED817B7C68AB7107483A/S107989860000158Xa.pdf/div-class-title-a-brief-introduction-to-algebraic-set-theory-div.pdf","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"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2062319438.pdf","grobid_xml":"https://content.openalex.org/works/W2062319438.grobid-xml"},"referenced_works_count":53,"referenced_works":["https://openalex.org/W36355091","https://openalex.org/W44595607","https://openalex.org/W89881250","https://openalex.org/W159183636","https://openalex.org/W177032397","https://openalex.org/W629880895","https://openalex.org/W786447156","https://openalex.org/W1498439614","https://openalex.org/W1512478964","https://openalex.org/W1528076413","https://openalex.org/W1557351111","https://openalex.org/W1580243564","https://openalex.org/W1732398793","https://openalex.org/W1786644787","https://openalex.org/W1976525497","https://openalex.org/W1977076690","https://openalex.org/W1983905931","https://openalex.org/W1995877143","https://openalex.org/W2023599931","https://openalex.org/W2043229226","https://openalex.org/W2045764924","https://openalex.org/W2049362364","https://openalex.org/W2054024574","https://openalex.org/W2058114039","https://openalex.org/W2062722679","https://openalex.org/W2092169546","https://openalex.org/W2094544397","https://openalex.org/W2098126895","https://openalex.org/W2112960774","https://openalex.org/W2120713972","https://openalex.org/W2121213425","https://openalex.org/W2122521516","https://openalex.org/W2130427934","https://openalex.org/W2137106928","https://openalex.org/W2144833073","https://openalex.org/W2152342937","https://openalex.org/W2169772316","https://openalex.org/W2170322156","https://openalex.org/W2291208220","https://openalex.org/W2485511814","https://openalex.org/W2498665769","https://openalex.org/W2499105636","https://openalex.org/W2509340638","https://openalex.org/W2551720480","https://openalex.org/W2610994252","https://openalex.org/W2740650585","https://openalex.org/W2950451231","https://openalex.org/W4251799386","https://openalex.org/W6622741888","https://openalex.org/W6649190667","https://openalex.org/W6674809377","https://openalex.org/W6680282017","https://openalex.org/W6685298461"],"related_works":["https://openalex.org/W2952078890","https://openalex.org/W4300880366","https://openalex.org/W2887094389","https://openalex.org/W2291208220","https://openalex.org/W2951427440","https://openalex.org/W4301022236","https://openalex.org/W2042945291","https://openalex.org/W2100490097","https://openalex.org/W4388940284","https://openalex.org/W1987689608"],"abstract_inverted_index":{"Abstract":[0],"This":[1],"brief":[2],"article":[3],"is":[4,34],"intended":[5],"to":[6,10,38,56,73],"introduce":[7],"the":[8,11,108],"reader":[9],"field":[12],"of":[13,20,23,81,102],"algebraic":[14,57,74],"set":[15,21,44,51,67,103],"theory,":[16],"in":[17,78],"which":[18,76],"models":[19,101],"theory":[22,95,104],"a":[24,79],"new":[25],"and":[26,42,87,99,107],"fascinating":[27],"kind":[28],"are":[29,54,69,105],"determined":[30],"algebraically.":[31],"The":[32],"method":[33],"quite":[35],"robust,":[36],"applying":[37],"various":[39],"classical,":[40],"intuitionistic,":[41],"constructive":[43],"theories.":[45],"Under":[46],"this":[47],"scheme":[48],"some":[49],"familiar":[50],"theoretic":[52],"properties":[53],"related":[55],"ones,":[58],"while":[59],"others":[60],"result":[61],"from":[62,93],"logical":[63],"constraints.":[64],"Conventional":[65],"elementary":[66],"theories":[68],"complete":[70],"with":[71],"respect":[72],"models,":[75],"arise":[77],"variety":[80],"ways,":[82],"such":[83,112],"as":[84],"topologically,":[85],"type-theoretically,":[86],"through":[88],"variation.":[89],"Many":[90],"previous":[91],"results":[92],"topos":[94],"involving":[96],"realizability,":[97],"permutation,":[98],"sheaf":[100],"subsumed,":[106],"prospects":[109],"for":[110],"further":[111],"unification":[113],"seem":[114],"bright.":[115]},"counts_by_year":[{"year":2022,"cited_by_count":2},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":3}],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2025-10-10T00:00:00"}