{"id":"https://openalex.org/W2059001666","doi":"https://doi.org/10.2307/2586591","title":"Uniformization and skolem functions in the class of trees","display_name":"Uniformization and skolem functions in the class of trees","publication_year":1998,"publication_date":"1998-03-01","ids":{"openalex":"https://openalex.org/W2059001666","doi":"https://doi.org/10.2307/2586591","mag":"2059001666"},"language":"en","primary_location":{"id":"doi:10.2307/2586591","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2586591","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/A5058233899","display_name":"Shmuel Lifsches","orcid":null},"institutions":[{"id":"https://openalex.org/I197251160","display_name":"Hebrew University of Jerusalem","ror":"https://ror.org/03qxff017","country_code":"IL","type":"education","lineage":["https://openalex.org/I197251160"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Shmuel Lifsches","raw_affiliation_strings":["Institute of Mathematics, The Hebrew University, Jerusalem, Israel, E-mail:"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Mathematics, The Hebrew University, Jerusalem, Israel, E-mail:","institution_ids":["https://openalex.org/I197251160"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5024923217","display_name":"Saharon Shelah","orcid":"https://orcid.org/0000-0003-0462-3152"},"institutions":[{"id":"https://openalex.org/I197251160","display_name":"Hebrew University of Jerusalem","ror":"https://ror.org/03qxff017","country_code":"IL","type":"education","lineage":["https://openalex.org/I197251160"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Saharon Shelah","raw_affiliation_strings":["Institute of Mathematics, The Hebrew University, Jerusalem, Israel, E-mail:"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Mathematics, The Hebrew University, Jerusalem, Israel, E-mail:","institution_ids":["https://openalex.org/I197251160"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I197251160"],"apc_list":null,"apc_paid":null,"fwci":0.4658,"has_fulltext":false,"cited_by_count":25,"citation_normalized_percentile":{"value":0.61928208,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"63","issue":"1","first_page":"103","last_page":"127"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9994000196456909,"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":0.9994000196456909,"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":0.996399998664856,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.9918000102043152,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.7533202767372131},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7083985805511475},{"id":"https://openalex.org/keywords/uniformization","display_name":"Uniformization (probability theory)","score":0.6769957542419434},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.6122188568115234},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5371912121772766},{"id":"https://openalex.org/keywords/subclass","display_name":"Subclass","score":0.4501490592956543},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.447870135307312},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4086950123310089},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.21788224577903748},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.099924236536026},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.07306718826293945}],"concepts":[{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.7533202767372131},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7083985805511475},{"id":"https://openalex.org/C149260544","wikidata":"https://www.wikidata.org/wiki/Q7885142","display_name":"Uniformization (probability theory)","level":5,"score":0.6769957542419434},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.6122188568115234},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5371912121772766},{"id":"https://openalex.org/C2776194381","wikidata":"https://www.wikidata.org/wiki/Q3965271","display_name":"Subclass","level":3,"score":0.4501490592956543},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.447870135307312},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4086950123310089},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.21788224577903748},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.099924236536026},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.07306718826293945},{"id":"https://openalex.org/C158917313","wikidata":"https://www.wikidata.org/wiki/Q4849964","display_name":"Balance equation","level":4,"score":0.0},{"id":"https://openalex.org/C163836022","wikidata":"https://www.wikidata.org/wiki/Q6771326","display_name":"Markov model","level":3,"score":0.0},{"id":"https://openalex.org/C203014093","wikidata":"https://www.wikidata.org/wiki/Q101929","display_name":"Immunology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C159654299","wikidata":"https://www.wikidata.org/wiki/Q79460","display_name":"Antibody","level":2,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.2307/2586591","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2586591","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/1183745461","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1183745461","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":10,"referenced_works":["https://openalex.org/W251225716","https://openalex.org/W1511526676","https://openalex.org/W1964766966","https://openalex.org/W2062792526","https://openalex.org/W2105322061","https://openalex.org/W2162583406","https://openalex.org/W2170458819","https://openalex.org/W4212901716","https://openalex.org/W4240244556","https://openalex.org/W6641740895"],"related_works":["https://openalex.org/W3135151721","https://openalex.org/W1994169959","https://openalex.org/W316900803","https://openalex.org/W2025265121","https://openalex.org/W2020531058","https://openalex.org/W2037210200","https://openalex.org/W1511067427","https://openalex.org/W2060980616","https://openalex.org/W2009011029","https://openalex.org/W4223613971"],"abstract_inverted_index":{"Abstract":[0],"The":[1],"monadic":[2,36],"second-order":[3],"theory":[4],"of":[5,19,65,78,82],"trees":[6,20,66],"allows":[7],"quantification":[8],"over":[9,12],"elements":[10],"and":[11,59],"arbitrary":[13],"subsets.":[14],"We":[15],"classify":[16],"the":[17,24,44,63,72,76],"class":[18,64],"with":[21,38,49,67],"respect":[22,50],"to":[23,51,61],"question:":[25],"does":[26],"a":[27,35],"tree":[28],"T":[29],"have":[30],"definable":[31,68,79],"Skolem":[32,69],"functions":[33],"(by":[34],"formula":[37],"parameters)?":[39],"This":[40],"continues":[41],"[6]":[42],"where":[43],"question":[45],"was":[46],"asked":[47],"only":[48],"choice":[52],"functions.":[53,70],"A":[54],"natural":[55],"subclass":[56],"is":[57],"defined":[58],"proved":[60],"be":[62],"Along":[71],"way":[73],"we":[74],"investigate":[75],"spectrum":[77],"well":[80,83],"orderings":[81],"ordered":[84],"chains.":[85]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
