{"title":"Filter logics: Filters on ω1","authors":"Matt Kaufmann","doi":"10.1016/0003-4843(81)90002-4","DOIUrl":null,"url":null,"abstract":"<div><p>Compactness and completeness theorems are proved for logics with a new quantifier M, whose interpretation depends on the choice of a filter on <em>ω</em><sub>1</sub>. Omitting types theorems and extensions to structures of arbitrary cardinality are also discussed. A number of questions are raised.</p></div>","PeriodicalId":100093,"journal":{"name":"Annals of Mathematical Logic","volume":"20 2","pages":"Pages 155-200"},"PeriodicalIF":0.0000,"publicationDate":"1981-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0003-4843(81)90002-4","citationCount":"4","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annals of Mathematical Logic","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/0003484381900024","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 4
Abstract
Compactness and completeness theorems are proved for logics with a new quantifier M, whose interpretation depends on the choice of a filter on ω1. Omitting types theorems and extensions to structures of arbitrary cardinality are also discussed. A number of questions are raised.
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