{"title":"Compactness of $\\omega^\\lambda$ for $\\lambda$ singular","authors":"P. Lipparini","doi":"10.4115/jla.v6i0.205","DOIUrl":null,"url":null,"abstract":"We characterize the compactness properties of the product of λ copies \nof the space ω with the discrete topology, dealing in particular with the case λ \nsingular, using regular and uniform ultrafilters, infinitary languages and nonstandard \nelements. We also deal with products of uncountable regular cardinals with the \norder topology.","PeriodicalId":53872,"journal":{"name":"Journal of Logic and Analysis","volume":null,"pages":null},"PeriodicalIF":0.3000,"publicationDate":"2013-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Logic and Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4115/jla.v6i0.205","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"LOGIC","Score":null,"Total":0}
引用次数: 1
Abstract
We characterize the compactness properties of the product of λ copies
of the space ω with the discrete topology, dealing in particular with the case λ
singular, using regular and uniform ultrafilters, infinitary languages and nonstandard
elements. We also deal with products of uncountable regular cardinals with the
order topology.
期刊介绍:
"Journal of Logic and Analysis" publishes papers of high quality involving interaction between ideas or techniques from mathematical logic and other areas of mathematics (especially - but not limited to - pure and applied analysis). The journal welcomes papers in nonstandard analysis and related areas of applied model theory; papers involving interplay between mathematics and logic (including foundational aspects of such interplay); mathematical papers using or developing analytical methods having connections to any area of mathematical logic. "Journal of Logic and Analysis" is intended to be a natural home for papers with an essential interaction between mathematical logic and other areas of mathematics, rather than for papers purely in logic or analysis.