{"id":"https://openalex.org/W1981694349","doi":"https://doi.org/10.1142/s0219061305000407","title":"SET MAPPING REFLECTION","display_name":"SET MAPPING REFLECTION","publication_year":2005,"publication_date":"2005-06-01","ids":{"openalex":"https://openalex.org/W1981694349","doi":"https://doi.org/10.1142/s0219061305000407","mag":"1981694349"},"language":"en","primary_location":{"id":"doi:10.1142/s0219061305000407","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0219061305000407","pdf_url":null,"source":{"id":"https://openalex.org/S29890666","display_name":"Journal of Mathematical Logic","issn_l":"0219-0613","issn":["0219-0613","1793-6691"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Mathematical Logic","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/math/0501526","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5002552785","display_name":"Justin Tatch Moore","orcid":"https://orcid.org/0000-0003-2107-8547"},"institutions":[{"id":"https://openalex.org/I120156002","display_name":"Boise State University","ror":"https://ror.org/02e3zdp86","country_code":"US","type":"education","lineage":["https://openalex.org/I120156002"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"JUSTIN TATCH MOORE","raw_affiliation_strings":["Department of Mathematics, Boise State University, Boise, Idaho 83725, USA","Department of Mathematics; Boise State University; Boise; Idaho; 83725; USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Boise State University, Boise, Idaho 83725, USA","institution_ids":["https://openalex.org/I120156002"]},{"raw_affiliation_string":"Department of Mathematics; Boise State University; Boise; Idaho; 83725; USA","institution_ids":["https://openalex.org/I120156002"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5002552785"],"corresponding_institution_ids":["https://openalex.org/I120156002"],"apc_list":null,"apc_paid":null,"fwci":7.5308,"has_fulltext":false,"cited_by_count":68,"citation_normalized_percentile":{"value":0.98139736,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"05","issue":"01","first_page":"87","last_page":"97"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9998000264167786,"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":0.9998000264167786,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9969000220298767,"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"}},{"id":"https://openalex.org/T13400","display_name":"Mathematical and Theoretical Analysis","score":0.9904000163078308,"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/forcing","display_name":"Forcing (mathematics)","score":0.8402101993560791},{"id":"https://openalex.org/keywords/axiom","display_name":"Axiom","score":0.7927075624465942},{"id":"https://openalex.org/keywords/axiom-of-choice","display_name":"Axiom of choice","score":0.7737226486206055},{"id":"https://openalex.org/keywords/reflection-principle","display_name":"Reflection principle (Wiener process)","score":0.7675348520278931},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7523071765899658},{"id":"https://openalex.org/keywords/reflection","display_name":"Reflection (computer programming)","score":0.6962990164756775},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.6078596115112305},{"id":"https://openalex.org/keywords/zermelo\u2013fraenkel-set-theory","display_name":"Zermelo\u2013Fraenkel set theory","score":0.5299564003944397},{"id":"https://openalex.org/keywords/constructive-set-theory","display_name":"Constructive set theory","score":0.5273205637931824},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5018854141235352},{"id":"https://openalex.org/keywords/set-theory","display_name":"Set theory","score":0.4170836806297302},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.39849376678466797},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.35461270809173584},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.34785592555999756},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.14263027906417847},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1353006660938263},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.0643802285194397}],"concepts":[{"id":"https://openalex.org/C197115733","wikidata":"https://www.wikidata.org/wiki/Q1003136","display_name":"Forcing (mathematics)","level":2,"score":0.8402101993560791},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.7927075624465942},{"id":"https://openalex.org/C151797676","wikidata":"https://www.wikidata.org/wiki/Q179692","display_name":"Axiom of choice","level":4,"score":0.7737226486206055},{"id":"https://openalex.org/C118368358","wikidata":"https://www.wikidata.org/wiki/Q7307248","display_name":"Reflection principle (Wiener process)","level":5,"score":0.7675348520278931},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7523071765899658},{"id":"https://openalex.org/C65682993","wikidata":"https://www.wikidata.org/wiki/Q1056451","display_name":"Reflection (computer programming)","level":2,"score":0.6962990164756775},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6078596115112305},{"id":"https://openalex.org/C51460","wikidata":"https://www.wikidata.org/wiki/Q191849","display_name":"Zermelo\u2013Fraenkel set theory","level":5,"score":0.5299564003944397},{"id":"https://openalex.org/C556429856","wikidata":"https://www.wikidata.org/wiki/Q5164501","display_name":"Constructive set theory","level":5,"score":0.5273205637931824},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5018854141235352},{"id":"https://openalex.org/C153046414","wikidata":"https://www.wikidata.org/wiki/Q12482","display_name":"Set theory","level":3,"score":0.4170836806297302},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.39849376678466797},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.35461270809173584},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.34785592555999756},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.14263027906417847},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1353006660938263},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0643802285194397},{"id":"https://openalex.org/C101615488","wikidata":"https://www.wikidata.org/wiki/Q1503307","display_name":"Geometric Brownian motion","level":4,"score":0.0},{"id":"https://openalex.org/C3017618536","wikidata":"https://www.wikidata.org/wiki/Q304994","display_name":"Innovation diffusion","level":2,"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/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C68710425","wikidata":"https://www.wikidata.org/wiki/Q5275442","display_name":"Diffusion process","level":3,"score":0.0},{"id":"https://openalex.org/C56739046","wikidata":"https://www.wikidata.org/wiki/Q192060","display_name":"Knowledge management","level":1,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1142/s0219061305000407","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0219061305000407","pdf_url":null,"source":{"id":"https://openalex.org/S29890666","display_name":"Journal of Mathematical Logic","issn_l":"0219-0613","issn":["0219-0613","1793-6691"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Mathematical Logic","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:math/0501526","is_oa":true,"landing_page_url":"http://arxiv.org/abs/math/0501526","pdf_url":"https://arxiv.org/pdf/math/0501526","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"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":null,"raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.637.1609","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.637.1609","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.cornell.edu/~justin/Ftp/MRP.pdf","raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:math/0501526","is_oa":true,"landing_page_url":"http://arxiv.org/abs/math/0501526","pdf_url":"https://arxiv.org/pdf/math/0501526","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"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":null,"raw_type":"text"},"sustainable_development_goals":[{"score":0.4399999976158142,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W81494948","https://openalex.org/W187570007","https://openalex.org/W588060734","https://openalex.org/W1427302000","https://openalex.org/W1591627679","https://openalex.org/W1595388840","https://openalex.org/W1601878490","https://openalex.org/W2070702249","https://openalex.org/W2070851509","https://openalex.org/W2079540958","https://openalex.org/W2087518766","https://openalex.org/W2090425123","https://openalex.org/W2111190351","https://openalex.org/W2117873821","https://openalex.org/W2122092051","https://openalex.org/W2152989620","https://openalex.org/W2159437191","https://openalex.org/W2214879377","https://openalex.org/W2319297044","https://openalex.org/W2492513299","https://openalex.org/W2577940507","https://openalex.org/W3151639028","https://openalex.org/W4206414785","https://openalex.org/W4232053157","https://openalex.org/W4234476515","https://openalex.org/W4238977241","https://openalex.org/W4243262771","https://openalex.org/W4250230991","https://openalex.org/W4250747102","https://openalex.org/W4302529523"],"related_works":["https://openalex.org/W1574825745","https://openalex.org/W2016661762","https://openalex.org/W2079743999","https://openalex.org/W2060433450","https://openalex.org/W2007535202","https://openalex.org/W1538212383","https://openalex.org/W2017481539","https://openalex.org/W102647493","https://openalex.org/W4243217895","https://openalex.org/W3197691547"],"abstract_inverted_index":{"In":[0],"this":[1,57],"note":[2],"we":[3],"will":[4,20,52],"discuss":[5],"a":[6],"new":[7],"reflection":[8,58],"principle":[9,59],"which":[10],"follows":[11],"from":[12],"the":[13,25,29,47],"Proper":[14,30],"Forcing":[15,31],"Axiom.":[16],"The":[17],"immediate":[18],"purpose":[19],"be":[21,54],"to":[22],"prove":[23],"that":[24,35,42,56,61],"bounded":[26],"form":[27],"of":[28,49],"Axiom":[32,48],"implies":[33,60],"both":[34],"2":[36,40],"\u03c9":[37,39,69],"=":[38],"and":[41],"[Formula:":[43],"see":[44],"text]":[45],"satisfies":[46],"Choice.":[50],"It":[51],"also":[53],"demonstrated":[55],"\u25a1(\u03ba)":[62],"fails":[63],"for":[64],"all":[65],"regular":[66],"\u03ba":[67],">":[68],"1":[70],".":[71]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":3},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":6},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}