{"title":"Parametrizing by the Ellentuck space","authors":"Timothy Trujillo","doi":"10.4064/fm86-6-2021","DOIUrl":null,"url":null,"abstract":"We introduce a new construct that can be used to parametrize a topological Ramsey space by the collection of infinite subsets of natural numbers. We show that these parametrized spaces are topological Ramsey spaces. Then we prove a canonical Ramsey theorem for some of the parametrized spaces arising from the construction and conclude with some open questions concerning applications of these canonical Ramsey theorems to the Tukey theory of ultrafilters.","PeriodicalId":55138,"journal":{"name":"Fundamenta Mathematicae","volume":"1 1","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Fundamenta Mathematicae","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4064/fm86-6-2021","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
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Abstract
We introduce a new construct that can be used to parametrize a topological Ramsey space by the collection of infinite subsets of natural numbers. We show that these parametrized spaces are topological Ramsey spaces. Then we prove a canonical Ramsey theorem for some of the parametrized spaces arising from the construction and conclude with some open questions concerning applications of these canonical Ramsey theorems to the Tukey theory of ultrafilters.
期刊介绍：
FUNDAMENTA MATHEMATICAE concentrates on papers devoted to
Set Theory,
Mathematical Logic and Foundations of Mathematics,
Topology and its Interactions with Algebra,
Dynamical Systems.
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