{"id":"https://openalex.org/W2034021457","doi":"https://doi.org/10.1016/0168-0072(93)90078-r","title":"Game sentences and ultrapowers","display_name":"Game sentences and ultrapowers","publication_year":1993,"publication_date":"1993-05-01","ids":{"openalex":"https://openalex.org/W2034021457","doi":"https://doi.org/10.1016/0168-0072(93)90078-r","mag":"2034021457"},"language":"en","primary_location":{"id":"doi:10.1016/0168-0072(93)90078-r","is_oa":false,"landing_page_url":"https://doi.org/10.1016/0168-0072(93)90078-r","pdf_url":null,"source":{"id":"https://openalex.org/S172477885","display_name":"Annals of Pure and Applied Logic","issn_l":"0168-0072","issn":["0168-0072","1873-2461"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Annals of Pure and Applied 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/A5050539424","display_name":"Renling Jin","orcid":"https://orcid.org/0000-0002-1625-1539"},"institutions":[{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Renling Jin","raw_affiliation_strings":["Department of Mathematics, University of California, Berkeley, CA 94720, USA","Department of Mathematics, University of California, Berkeley CA 94720, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of California, Berkeley, CA 94720, USA","institution_ids":["https://openalex.org/I95457486"]},{"raw_affiliation_string":"Department of Mathematics, University of California, Berkeley CA 94720, USA","institution_ids":["https://openalex.org/I95457486"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5009762723","display_name":"H. Jerome Keisler","orcid":"https://orcid.org/0009-0007-1747-1393"},"institutions":[{"id":"https://openalex.org/I135310074","display_name":"University of Wisconsin\u2013Madison","ror":"https://ror.org/01y2jtd41","country_code":"US","type":"education","lineage":["https://openalex.org/I135310074"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"H.Jerome Keisler","raw_affiliation_strings":["Department of Mathematics, University of Wisconsin, Madison, WI 53706, USA","Department of Mathematics, University of Wisconsin-Madison, WI 53706, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Wisconsin, Madison, WI 53706, USA","institution_ids":["https://openalex.org/I135310074"]},{"raw_affiliation_string":"Department of Mathematics, University of Wisconsin-Madison, WI 53706, USA","institution_ids":["https://openalex.org/I135310074"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5050539424"],"corresponding_institution_ids":["https://openalex.org/I95457486"],"apc_list":{"value":3390,"currency":"USD","value_usd":3390},"apc_paid":null,"fwci":1.7524,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.82273021,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"60","issue":"3","first_page":"261","last_page":"274"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13400","display_name":"Mathematical and Theoretical Analysis","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T13400","display_name":"Mathematical and Theoretical Analysis","score":0.9998000264167786,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9983000159263611,"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/T11151","display_name":"Advanced Topology and Set Theory","score":0.9948999881744385,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/ultraproduct","display_name":"Ultraproduct","score":0.8293954133987427},{"id":"https://openalex.org/keywords/ultrafilter","display_name":"Ultrafilter","score":0.5824504494667053},{"id":"https://openalex.org/keywords/sentence","display_name":"Sentence","score":0.55043625831604},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5246034860610962},{"id":"https://openalex.org/keywords/expressive-power","display_name":"Expressive power","score":0.4892723262310028},{"id":"https://openalex.org/keywords/sequential-game","display_name":"Sequential game","score":0.42242902517318726},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.33112460374832153},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.33038830757141113},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.308963418006897},{"id":"https://openalex.org/keywords/game-theory","display_name":"Game theory","score":0.24645042419433594},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.23155111074447632},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.22747087478637695}],"concepts":[{"id":"https://openalex.org/C167930466","wikidata":"https://www.wikidata.org/wiki/Q1535225","display_name":"Ultraproduct","level":2,"score":0.8293954133987427},{"id":"https://openalex.org/C87598191","wikidata":"https://www.wikidata.org/wiki/Q1571831","display_name":"Ultrafilter","level":2,"score":0.5824504494667053},{"id":"https://openalex.org/C2777530160","wikidata":"https://www.wikidata.org/wiki/Q41796","display_name":"Sentence","level":2,"score":0.55043625831604},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5246034860610962},{"id":"https://openalex.org/C195818886","wikidata":"https://www.wikidata.org/wiki/Q5421724","display_name":"Expressive power","level":2,"score":0.4892723262310028},{"id":"https://openalex.org/C73795354","wikidata":"https://www.wikidata.org/wiki/Q287618","display_name":"Sequential game","level":3,"score":0.42242902517318726},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.33112460374832153},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.33038830757141113},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.308963418006897},{"id":"https://openalex.org/C177142836","wikidata":"https://www.wikidata.org/wiki/Q44455","display_name":"Game theory","level":2,"score":0.24645042419433594},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.23155111074447632},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.22747087478637695}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/0168-0072(93)90078-r","is_oa":false,"landing_page_url":"https://doi.org/10.1016/0168-0072(93)90078-r","pdf_url":null,"source":{"id":"https://openalex.org/S172477885","display_name":"Annals of Pure and Applied Logic","issn_l":"0168-0072","issn":["0168-0072","1873-2461"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Annals of Pure and Applied Logic","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","score":0.5199999809265137,"display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W110169430","https://openalex.org/W138725251","https://openalex.org/W204330610","https://openalex.org/W1552606709","https://openalex.org/W1951287835","https://openalex.org/W1996613449","https://openalex.org/W2002971968","https://openalex.org/W2006781266","https://openalex.org/W2012497542","https://openalex.org/W2018381902","https://openalex.org/W2036951624","https://openalex.org/W2047612490","https://openalex.org/W2072087802","https://openalex.org/W2099041909","https://openalex.org/W2112149503","https://openalex.org/W2154942716","https://openalex.org/W2157276982","https://openalex.org/W2333748530","https://openalex.org/W2502726826","https://openalex.org/W2891745304","https://openalex.org/W6604374760","https://openalex.org/W6605581562","https://openalex.org/W6608275585","https://openalex.org/W6703076682","https://openalex.org/W6754737589"],"related_works":["https://openalex.org/W2147918975","https://openalex.org/W1980613621","https://openalex.org/W2897172575","https://openalex.org/W2002971968","https://openalex.org/W2059089698","https://openalex.org/W3101558303","https://openalex.org/W1966531754","https://openalex.org/W1987355600","https://openalex.org/W1606601082","https://openalex.org/W23083977"],"abstract_inverted_index":null,"counts_by_year":[{"year":2018,"cited_by_count":1}],"updated_date":"2026-03-10T14:07:55.174380","created_date":"2025-10-10T00:00:00"}