{"id":"https://openalex.org/W2137150069","doi":"https://doi.org/10.2307/2274903","title":"The structure of graphs all of whose <i>Y</i>-sections are internal sets","display_name":"The structure of graphs all of whose <i>Y</i>-sections are internal sets","publication_year":1991,"publication_date":"1991-03-01","ids":{"openalex":"https://openalex.org/W2137150069","doi":"https://doi.org/10.2307/2274903","mag":"2137150069"},"language":"en","primary_location":{"id":"doi:10.2307/2274903","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2274903","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/I1745920","display_name":"University of Wisconsin\u2013Platteville","ror":"https://ror.org/02xpkhc07","country_code":"US","type":"education","lineage":["https://openalex.org/I1745920"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Bo\u0161ko \u017divaljevi\u0107","raw_affiliation_strings":["Department of Mathematics, University of Wisconsin at Platteville, Platteville, Wisconsin 53818","University of Wisconsin at Platteville"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Wisconsin at Platteville, Platteville, Wisconsin 53818","institution_ids":["https://openalex.org/I1745920"]},{"raw_affiliation_string":"University of Wisconsin at Platteville","institution_ids":["https://openalex.org/I1745920"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5088197740"],"corresponding_institution_ids":["https://openalex.org/I1745920"],"apc_list":null,"apc_paid":null,"fwci":1.7142,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.86612082,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"56","issue":"1","first_page":"50","last_page":"66"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9979000091552734,"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":0.9979000091552734,"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":0.983299970626831,"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/mathematics","display_name":"Mathematics","score":0.5900550484657288},{"id":"https://openalex.org/keywords/cardinality","display_name":"Cardinality (data modeling)","score":0.5760766863822937},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.5329673290252686},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.4919848144054413},{"id":"https://openalex.org/keywords/universe","display_name":"Universe","score":0.47028377652168274},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.44338151812553406},{"id":"https://openalex.org/keywords/terminology","display_name":"Terminology","score":0.42039045691490173},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.41800791025161743},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.355388343334198},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.16674306988716125},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.13497665524482727},{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.12465086579322815},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.12210437655448914},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.10520350933074951},{"id":"https://openalex.org/keywords/linguistics","display_name":"Linguistics","score":0.10340523719787598}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5900550484657288},{"id":"https://openalex.org/C87117476","wikidata":"https://www.wikidata.org/wiki/Q362383","display_name":"Cardinality (data modeling)","level":2,"score":0.5760766863822937},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.5329673290252686},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.4919848144054413},{"id":"https://openalex.org/C84999194","wikidata":"https://www.wikidata.org/wiki/Q1","display_name":"Universe","level":2,"score":0.47028377652168274},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.44338151812553406},{"id":"https://openalex.org/C547195049","wikidata":"https://www.wikidata.org/wiki/Q1725664","display_name":"Terminology","level":2,"score":0.42039045691490173},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.41800791025161743},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.355388343334198},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.16674306988716125},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.13497665524482727},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.12465086579322815},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.12210437655448914},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10520350933074951},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.10340523719787598},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.0},{"id":"https://openalex.org/C44870925","wikidata":"https://www.wikidata.org/wiki/Q37547","display_name":"Astrophysics","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.2307/2274903","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2274903","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W566121181","https://openalex.org/W888228543","https://openalex.org/W1502653069","https://openalex.org/W1555991696","https://openalex.org/W1984628349","https://openalex.org/W1990582318","https://openalex.org/W2019014134","https://openalex.org/W2130476007","https://openalex.org/W2315435043","https://openalex.org/W2585712780"],"related_works":["https://openalex.org/W2350593162","https://openalex.org/W2390350206","https://openalex.org/W1969477129","https://openalex.org/W2921208823","https://openalex.org/W2131808775","https://openalex.org/W2353483812","https://openalex.org/W2360756181","https://openalex.org/W2374093222","https://openalex.org/W3154008094","https://openalex.org/W2485961789"],"abstract_inverted_index":{"The":[0],"purpose":[1],"of":[2,16,34,52,75,112,116,145,203,208,238,242,260,284,286,300,309,320,333],"this":[3,337],"paper":[4],"is":[5,95,152,191,217,246,257,273,317],"to":[6,39,119,136,155,162],"give":[7],"structural":[8,198],"results":[9,49],"on":[10,44],"graphs":[11,201],"lying":[12],"in":[13,72,131,142,171,222,271],"the":[14,40,73,92,124,143,183,188,197,214,228,239,269,287,295,301,331],"product":[15,74,144],"two":[17,76,146],"hyperfinite":[18],"sets":[19,31,78,148],"X":[20,79,149],"and":[21,54,61,80,128,150],"Y":[22,25,81,151,205,240,311],",":[23],"whose":[24,204,310],"-sections":[26,206,241,312],"are":[27,207,299,313],"either":[28],"all":[29,33,187,202,237,308],"internal":[30,77,88,117,147,157,179,251],"or":[32,278,291],"\u201csmall\u201d":[35],"cardinality":[36,209,243],"with":[37,236],"respect":[38],"saturation":[41,230],"assumption":[42],"imposed":[43],"our":[45,172],"nonstandard":[46,93,215],"universe.":[47],"These":[48],"generalize":[50],"those":[51],"[KKML]":[53,57],"[HeRo].":[55],"In":[56,266,330],"Keisler,":[58],"Kunen,":[59],"Miller":[60],"Leth":[62],"proved,":[63],"among":[64],"other":[65,125],"results,":[66],"that":[67,91,101,138,213],"any":[68,102,139,254,305],"countably":[69,86,103,113,120,321],"determined":[70,104,121],"function":[71,105,141,176],"can":[82,106],"be":[83,107],"covered":[84,247],"by":[85,195,248,340],"many":[87,114,322],"functions":[89,118,298,324],"provided":[90],"universe":[94,216],"at":[96,314],"least":[97],"\u2135-saturated.":[98],"This":[99],"shows":[100],"represented":[108],"as":[109],"a":[110,232,258,282,318],"union":[111,259,319],"restrictions":[115],"sets.":[122],"On":[123],"hand,":[126],"Henson":[127],"Ross":[129],"use":[130],"[HeRo]":[132],"Choquet's":[133],"capacitability":[134],"theorem":[135],"prove":[137],"Souslin":[140,175],"a.e.":[153,180],"equal":[154],"an":[156,163,178],"function.":[158],"(Here":[159],"\u201ca.e.\u201d":[160],"refers":[161],"arbitrary":[164],"but":[165],"fixed":[166],"bounded":[167],"Loeb":[168],"measure.)":[169],"Therefore,":[170,253],"terminology,":[173],"every":[174],"possesses":[177],"lifting.":[181],"After":[182],"introductory":[184],"\u00a70,":[185],"where":[186],"necessary":[189],"terminology":[190],"introduced,":[192],"we":[193],"continue":[194],"presenting":[196],"result":[199],"for":[200],"\u2264":[210,218,244],"\u03ba":[211,219,233,245,249,261,263,276,279,289],"(provided":[212],"+":[220],"-saturated)":[221],"\u00a71.":[223],"We":[224],"show":[225],"that,":[226],"under":[227],"above":[229],"assumption,":[231],"-determined":[234,264],"graph":[235,256,270,307],"-many":[250,262],"functions.":[252,265],"such":[255],"particular":[267],"if":[268],"question":[272],"Borel,":[274,288],"Souslin,":[275],"-Borel":[277,290],"-Souslin":[280],"(or":[281],"member":[283],"one":[285],"projective":[292],"hierarchies)":[293],"then":[294],"corresponding":[296],"constituting":[297],"same":[302],"\u201ccomplexity\u201d.":[303],"Thus,":[304],"Borel":[306,323,328],"most":[315],"countable":[316],"and,":[325],"consequently,":[326],"has":[327],"domain.":[329],"setting":[332],"Polish":[334],"topological":[335],"spaces":[336],"was":[338],"proved":[339],"Novikov":[341],"(see":[342],"[De]).":[343]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}