{"id":"https://openalex.org/W2130476007","doi":"https://doi.org/10.2307/2274650","title":"Some results about Borel sets in descriptive set theory of hyperfinite sets","display_name":"Some results about Borel sets in descriptive set theory of hyperfinite sets","publication_year":1990,"publication_date":"1990-06-01","ids":{"openalex":"https://openalex.org/W2130476007","doi":"https://doi.org/10.2307/2274650","mag":"2130476007"},"language":"en","primary_location":{"id":"doi:10.2307/2274650","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2274650","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/A5088197740","display_name":"Bo\u0161ko \u017divaljevi\u0107","orcid":null},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Bo\u0161ko \u017divaljevi\u0107","raw_affiliation_strings":["Department of Mathematics, University of Illinois, Urbana, Illinois 61801","Department of Mathematics, University of Illinois, Urbana, Illinois, 61801"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Illinois, Urbana, Illinois 61801","institution_ids":["https://openalex.org/I157725225"]},{"raw_affiliation_string":"Department of Mathematics, University of Illinois, Urbana, Illinois, 61801","institution_ids":["https://openalex.org/I157725225"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5088197740"],"corresponding_institution_ids":["https://openalex.org/I157725225"],"apc_list":null,"apc_paid":null,"fwci":2.6347,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.91704302,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":null,"biblio":{"volume":"55","issue":"2","first_page":"604","last_page":"614"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.995199978351593,"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"}},"topics":[{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.995199978351593,"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/T13400","display_name":"Mathematical and Theoretical Analysis","score":0.9775999784469604,"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"}},{"id":"https://openalex.org/T12137","display_name":"Economic theories and models","score":0.9307000041007996,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8729194402694702},{"id":"https://openalex.org/keywords/bijection","display_name":"Bijection","score":0.8568724393844604},{"id":"https://openalex.org/keywords/borel-measure","display_name":"Borel measure","score":0.5542077422142029},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.4688488245010376},{"id":"https://openalex.org/keywords/borel-set","display_name":"Borel set","score":0.45971301198005676},{"id":"https://openalex.org/keywords/countable-set","display_name":"Countable set","score":0.4528939127922058},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.42607834935188293},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.41856369376182556},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3414905071258545},{"id":"https://openalex.org/keywords/probability-measure","display_name":"Probability measure","score":0.2548522353172302}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8729194402694702},{"id":"https://openalex.org/C24424167","wikidata":"https://www.wikidata.org/wiki/Q180907","display_name":"Bijection","level":2,"score":0.8568724393844604},{"id":"https://openalex.org/C166758865","wikidata":"https://www.wikidata.org/wiki/Q892585","display_name":"Borel measure","level":3,"score":0.5542077422142029},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.4688488245010376},{"id":"https://openalex.org/C39952206","wikidata":"https://www.wikidata.org/wiki/Q21086747","display_name":"Borel set","level":2,"score":0.45971301198005676},{"id":"https://openalex.org/C110729354","wikidata":"https://www.wikidata.org/wiki/Q185478","display_name":"Countable set","level":2,"score":0.4528939127922058},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.42607834935188293},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.41856369376182556},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3414905071258545},{"id":"https://openalex.org/C21031990","wikidata":"https://www.wikidata.org/wiki/Q355020","display_name":"Probability measure","level":2,"score":0.2548522353172302},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.2307/2274650","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2274650","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/1183743317","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1183743317","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/W1499443856","https://openalex.org/W1555991696","https://openalex.org/W1984628349","https://openalex.org/W1990582318","https://openalex.org/W2019014134","https://openalex.org/W2047612490","https://openalex.org/W2315435043","https://openalex.org/W4230295967"],"related_works":["https://openalex.org/W4388321124","https://openalex.org/W4252375106","https://openalex.org/W2031042539","https://openalex.org/W1491956444","https://openalex.org/W2949346342","https://openalex.org/W1516336919","https://openalex.org/W2042364036","https://openalex.org/W4302605874","https://openalex.org/W2012071191","https://openalex.org/W2125136291"],"abstract_inverted_index":{"A":[0,72,77,108,123],"remarkable":[1],"result":[2,92,161],"of":[3,20,43,93,162,170,175],"Henson":[4,94,163],"and":[5,65,73,95,100,109,119,129,164,206,225,236],"Ross":[6,165],"[HR]":[7,235],"states":[8],"that":[9,55,67,104,138,184],"if":[10,118,121,205,208],"a":[11,32,87,114,148,193],"function":[12,59],"whose":[13,173],"graph":[14],"is":[15,127,177],"Souslin":[16,58,224],"in":[17,24,152],"the":[18,44,48,90,160,167,211,220,231],"product":[19],"two":[21,69,105,185],"hyperfinite":[22],"sets":[23,71,107,144,172],"an":[25,40],"\u2135":[26],"1":[27,82],"saturated":[28],"nonstandard":[29],"universe":[30],"possesses":[31],"certain":[33],"nice":[34],"property":[35],"(capacity)":[36],"then":[37],"there":[38],"exists":[39],"internal":[41,62,70,106,171],"subfunction":[42],"given":[45],"one":[46],"possessing":[47],"same":[49,212],"property.":[50],"In":[51,132],"particular,":[52],"they":[53,209],"prove":[54,183],"every":[56,68],"1-1":[57],"preserves":[60],"any":[61],"counting":[63,194,213],"measure,":[64],"show":[66,137],"B":[74,79,110,125],"with":[75,219],"\u2223":[76,80,122,126],"\u2223/\u2223":[78,124],"\u2248":[81],"are":[83,111,202],"Borel":[84,140,143,146,168,186,203],"bijective.":[85],"As":[86],"supplement":[88],"to":[89,180,188,198],"last-mentioned":[91],"Ross,":[96],"Keisler,":[97],"Kunen,":[98],"Miller":[99],"Leth":[101],"showed":[102],"[KKML]":[103],"bijective":[112,204],"by":[113],"countably":[115,227],"determined":[116,228],"bijection":[117],"only":[120,207],"finite":[128],"not":[130,196],"infinitesimal.":[131],"this":[133],"paper":[134],"we":[135,158,190],"first":[136],"injective":[139],"functions":[141],"map":[142],"into":[145],"sets,":[147,187,229],"fact":[149],"well":[150],"known":[151],"classical":[153],"descriptive":[154],"set":[155],"theory.":[156],"Then,":[157],"extend":[159],"concerning":[166],"bijectivity":[169],"quotient":[174],"cardinalities":[176],"infinitely":[178],"closed":[179],"1.":[181],"We":[182],"which":[189],"may":[191],"assign":[192],"measure":[195,214],"equal":[197],"0":[199],"or":[200],"\u221e,":[201],"have":[210],"\u22600,":[215],"\u221e.":[216],"This,":[217],"together":[218],"similar":[221],"characterization":[222],"for":[223],"measurable":[226],"extends":[230],"above-mentioned":[232],"results":[233],"from":[234],"[KKML].":[237]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
