{"title":"Partition subalgebras for maximal almost disjoint families","authors":"Alan Dow, Jinyuan Zhou","doi":"10.1016/S0168-0072(01)00120-8","DOIUrl":null,"url":null,"abstract":"<div><p>Partitioner algebras are defined by Baumgartner and Weese (Trans. Amer. Math. Soc. 274 (2) (1982) 619) as a natural tool for studying the properties of maximal almost disjoint families of subsets of <em>ω</em>. We prove from PFA<sup>+</sup> and ♢(<em>S</em><sub>0</sub><sup>2</sup>) that there exists a partitioner algebra which contains a subalgebra which is not representable as a partitioner algebra.</p></div>","PeriodicalId":50762,"journal":{"name":"Annals of Pure and Applied Logic","volume":"117 1","pages":"Pages 223-259"},"PeriodicalIF":0.6000,"publicationDate":"2002-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0168-0072(01)00120-8","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annals of Pure and Applied Logic","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0168007201001208","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2001/11/30 0:00:00","PubModel":"Epub","JCR":"Q2","JCRName":"LOGIC","Score":null,"Total":0}
引用次数: 2
Abstract
Partitioner algebras are defined by Baumgartner and Weese (Trans. Amer. Math. Soc. 274 (2) (1982) 619) as a natural tool for studying the properties of maximal almost disjoint families of subsets of ω. We prove from PFA+ and ♢(S02) that there exists a partitioner algebra which contains a subalgebra which is not representable as a partitioner algebra.
期刊介绍：
The journal Annals of Pure and Applied Logic publishes high quality papers in all areas of mathematical logic as well as applications of logic in mathematics, in theoretical computer science and in other related disciplines. All submissions to the journal should be mathematically correct, well written (preferably in English)and contain relevant new results that are of significant interest to a substantial number of logicians. The journal also considers submissions that are somewhat too long to be published by other journals while being too short to form a separate memoir provided that they are of particular outstanding quality and broad interest. In addition, Annals of Pure and Applied Logic occasionally publishes special issues of selected papers from well-chosen conferences in pure and applied logic.
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