{"id":"https://openalex.org/W4414826355","doi":"https://doi.org/10.1017/bsl.2025.10109","title":"O <scp>brad</scp> K <scp>asum</scp> . <i> <b>Investigation into phenomena surrounding universally Baire sets.</b> </i> Universit\u00e9 Paris Cit\u00e9. 2025. Supervised by Boban Veli\u010dkovi\u0107, Grigor Sargsyan. MSC: 03E40, 03E45, 03E55, 03E57, 03E60. Keywords: universally Baire sets, determinacy, $\\mathsf {HOD}$, mice, hod mice, Chang-plus model, stationary-set-preserving, Model Existence Game, $\\mathbb {P}_{\\max }$, generic absoluteness, generic maximality.","display_name":"O <scp>brad</scp> K <scp>asum</scp> . <i> <b>Investigation into phenomena surrounding universally Baire sets.</b> </i> Universit\u00e9 Paris Cit\u00e9. 2025. Supervised by Boban Veli\u010dkovi\u0107, Grigor Sargsyan. MSC: 03E40, 03E45, 03E55, 03E57, 03E60. Keywords: universally Baire sets, determinacy, $\\mathsf {HOD}$, mice, hod mice, Chang-plus model, stationary-set-preserving, Model Existence Game, $\\mathbb {P}_{\\max }$, generic absoluteness, generic maximality.","publication_year":2025,"publication_date":"2025-12-01","ids":{"openalex":"https://openalex.org/W4414826355","doi":"https://doi.org/10.1017/bsl.2025.10109"},"language":"en","primary_location":{"id":"doi:10.1017/bsl.2025.10109","is_oa":true,"landing_page_url":"https://doi.org/10.1017/bsl.2025.10109","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/B1978BBECC36309E298E5B48D3CC0E70/S1079898625101091a.pdf/div-class-title-investigation-into-phenomena-surrounding-universally-baire-sets-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":"The Bulletin of Symbolic Logic","raw_type":"journal-article"},"type":"dissertation","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/B1978BBECC36309E298E5B48D3CC0E70/S1079898625101091a.pdf/div-class-title-investigation-into-phenomena-surrounding-universally-baire-sets-div.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5119847486","display_name":"Obrad Kasum","orcid":null},"institutions":[{"id":"https://openalex.org/I204730241","display_name":"Universit\u00e9 Paris Cit\u00e9","ror":"https://ror.org/05f82e368","country_code":"FR","type":"education","lineage":["https://openalex.org/I204730241"]},{"id":"https://openalex.org/I4210091437","display_name":"Sorbonne Paris Cit\u00e9","ror":"https://ror.org/001z21q04","country_code":"FR","type":"other","lineage":["https://openalex.org/I4210091437"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Obrad Kasum","raw_affiliation_strings":["Universit\u00e9 Paris Cit\u00e9. 2025"],"affiliations":[{"raw_affiliation_string":"Universit\u00e9 Paris Cit\u00e9. 2025","institution_ids":["https://openalex.org/I204730241","https://openalex.org/I4210091437"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5119847486"],"corresponding_institution_ids":["https://openalex.org/I204730241","https://openalex.org/I4210091437"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.29969706,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"31","issue":"4","first_page":"695","last_page":"696"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12122","display_name":"Physical Unclonable Functions (PUFs) and Hardware Security","score":0.70660001039505,"subfield":{"id":"https://openalex.org/subfields/1708","display_name":"Hardware and Architecture"},"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/T12122","display_name":"Physical Unclonable Functions (PUFs) and Hardware Security","score":0.70660001039505,"subfield":{"id":"https://openalex.org/subfields/1708","display_name":"Hardware and Architecture"},"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/class","display_name":"Class (philosophy)","score":0.5849999785423279},{"id":"https://openalex.org/keywords/absoluteness","display_name":"Absoluteness","score":0.5843999981880188},{"id":"https://openalex.org/keywords/baire-space","display_name":"Baire space","score":0.5611000061035156},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.524399995803833},{"id":"https://openalex.org/keywords/relation","display_name":"Relation (database)","score":0.5232999920845032},{"id":"https://openalex.org/keywords/nowhere-dense-set","display_name":"Nowhere dense set","score":0.5062000155448914},{"id":"https://openalex.org/keywords/baire-measure","display_name":"Baire measure","score":0.4799000024795532},{"id":"https://openalex.org/keywords/baire-category-theorem","display_name":"Baire category theorem","score":0.4690000116825104}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7760999798774719},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5849999785423279},{"id":"https://openalex.org/C2780102774","wikidata":"https://www.wikidata.org/wiki/Q4669873","display_name":"Absoluteness","level":2,"score":0.5843999981880188},{"id":"https://openalex.org/C166359235","wikidata":"https://www.wikidata.org/wiki/Q1150180","display_name":"Baire space","level":2,"score":0.5611000061035156},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.524399995803833},{"id":"https://openalex.org/C25343380","wikidata":"https://www.wikidata.org/wiki/Q277521","display_name":"Relation (database)","level":2,"score":0.5232999920845032},{"id":"https://openalex.org/C17327563","wikidata":"https://www.wikidata.org/wiki/Q1991405","display_name":"Nowhere dense set","level":3,"score":0.5062000155448914},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4875999987125397},{"id":"https://openalex.org/C189892329","wikidata":"https://www.wikidata.org/wiki/Q2577940","display_name":"Baire measure","level":2,"score":0.4799000024795532},{"id":"https://openalex.org/C44659138","wikidata":"https://www.wikidata.org/wiki/Q1052678","display_name":"Baire category theorem","level":2,"score":0.4690000116825104},{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.4677000045776367},{"id":"https://openalex.org/C153046414","wikidata":"https://www.wikidata.org/wiki/Q12482","display_name":"Set theory","level":3,"score":0.387800008058548},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.38260000944137573},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.37540000677108765},{"id":"https://openalex.org/C42357961","wikidata":"https://www.wikidata.org/wiki/Q213363","display_name":"Open set","level":2,"score":0.34860000014305115},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.328000009059906},{"id":"https://openalex.org/C184264201","wikidata":"https://www.wikidata.org/wiki/Q21199","display_name":"Natural number","level":2,"score":0.3046000003814697},{"id":"https://openalex.org/C61067352","wikidata":"https://www.wikidata.org/wiki/Q1897429","display_name":"Ultrametric space","level":3,"score":0.2773999869823456},{"id":"https://openalex.org/C168167062","wikidata":"https://www.wikidata.org/wiki/Q1117970","display_name":"Component (thermodynamics)","level":2,"score":0.2734000086784363},{"id":"https://openalex.org/C47030870","wikidata":"https://www.wikidata.org/wiki/Q467606","display_name":"Model theory","level":2,"score":0.2671999931335449},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.2605000138282776},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.25360000133514404}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1017/bsl.2025.10109","is_oa":true,"landing_page_url":"https://doi.org/10.1017/bsl.2025.10109","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/B1978BBECC36309E298E5B48D3CC0E70/S1079898625101091a.pdf/div-class-title-investigation-into-phenomena-surrounding-universally-baire-sets-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":"The Bulletin of Symbolic Logic","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1017/bsl.2025.10109","is_oa":true,"landing_page_url":"https://doi.org/10.1017/bsl.2025.10109","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/B1978BBECC36309E298E5B48D3CC0E70/S1079898625101091a.pdf/div-class-title-investigation-into-phenomena-surrounding-universally-baire-sets-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":"The 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/W4414826355.pdf","grobid_xml":"https://content.openalex.org/works/W4414826355.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Abstract":[0,291],"This":[1,95],"thesis":[2,296],"presents":[3],"my":[4],"contributions":[5],"to":[6,43,99,238],"various":[7],"aspects":[8,19],"of":[9,12,17,31,60,85,106,110,124,153,159,165,173,183,186,243,247,266,273,288],"the":[10,21,107,135,145,163,184,191,232,240,274,295],"theory":[11,185],"universally":[13,34,88,179,187,210,226],"Baire":[14,35,89,188,211,227],"sets.":[15],"One":[16],"these":[18],"is":[20,127,132,178,190,270],"smallest":[22],"inner":[23,45],"model":[24,46,109,131,246],"containing":[25],"all":[26,29],"reals":[27,32],"whose":[28,176],"sets":[30,90,189,212,228],"are":[33,157,236],"(viz.,":[36],"$L(\\mathbb":[37,64,76],"{R})$":[38,65,77],")":[39,117],"and":[40,194],"its":[41,44,69],"relation":[42],"$\\mathsf":[47,54,111],"{HOD}$":[48],".":[49,78,121],"We":[50,79,199,259,278],"verify":[51],"here":[52],"that":[53,128,149],"{HOD}^{L(\\mathbb":[55],"{R})}$":[56],"enjoys":[57],"a":[58,72,82,150,166,170,245,256,267,271,281],"form":[59],"local":[61],"definability":[62],"inside":[63],",":[66],"further":[67],"justifying":[68],"characterization":[70],"as":[71,213,217,219,229],"\u201ccore":[73],"model\u201d":[74],"in":[75,134,264,286],"then":[80,279],"study":[81],"\u201cbottom-up\u201d":[83],"construction":[84,96],"more":[86],"complicated":[87],"(more":[91],"generally,":[92],"determined":[93],"sets).":[94],"allows":[97],"us":[98],"give":[100,280],"an":[101,248],"\u201c":[102],"L":[103],"-like\u201d":[104],"description":[105,126],"minimum":[108,130],"{AD}_{\\mathbb":[112],"{R}}":[113],"+":[114],"\\mathsf":[115],"{Cof}(\\Theta":[116],"=":[118],"\\Theta":[119],"$":[120],"A":[122],"consequence":[123],"this":[125,129,262,285],"contained":[133],"Chang-plus":[136,146],"model.":[137],"Our":[138],"construction,":[139],"together":[140],"with":[141,169,197,209,225],"Woodin\u2019s":[142],"work":[143],"on":[144],"model,":[147],"shows":[148],"proper":[151],"class":[152],"Woodin":[154,160,174],"cardinals":[155,161,175],"which":[156,269],"limits":[158],"implies":[162],"existence":[164],"hod":[167],"mouse":[168],"measurable":[171],"limit":[172],"strategy":[177],"Baire.":[180],"Another":[181],"aspect":[182],"generic":[192,204,220,289],"absoluteness":[193],"maximality":[195],"associated":[196],"them.":[198],"include":[200],"some":[201],"results":[202],"concerning":[203],"$\\Sigma":[205],"_1^{H(\\omega":[206],"_2)}$":[207,223],"-absoluteness":[208],"predicates":[214],"or":[215],"parameters,":[216],"well":[218],"$\\Pi":[221],"_2^{H(\\omega":[222],"-maximality":[224],"predicates.":[230],"In":[231],"second":[233],"case,":[234],"we":[235],"led":[237],"consider":[239],"general":[241],"question":[242],"when":[244,261],"infinitary":[249],"propositional":[250],"formula":[251],"can":[252],"be":[253],"added":[254],"by":[255],"stationary-set-preserving":[257],"poset.":[258],"characterize":[260],"happens":[263],"terms":[265,287],"game":[268],"variant":[272],"Model":[275],"Existence":[276],"Game.":[277],"sufficient":[282],"condition":[283],"for":[284],"embeddings.":[290],"taken":[292],"directly":[293],"from":[294],"E-mail:":[297],"obrad@math.ucla.edu":[298],"URL":[299],":":[300],"https://hal.science/view/index/docid/5273407":[301]},"counts_by_year":[],"updated_date":"2026-03-25T13:04:00.132906","created_date":"2025-10-05T00:00:00"}