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dc.contributor.authorDobrinen, Natashaen
dc.contributor.authorTodorčević, Stevoen
dc.date.accessioned2020-05-01T20:29:23Z-
dc.date.available2020-05-01T20:29:23Z-
dc.date.issued2013-09-09en
dc.identifier.issn1571-0653-
dc.identifier.urihttp://researchrepository.mi.sanu.ac.rs/handle/123456789/2197-
dc.description.abstractMotivated by Tukey classification problems, we develop a new hierarchy of topological Ramsey spaces Rα,α<ω1. These spaces form a natural hierarchy of complexity, R0 being the Ellentuck space [Erik Ellentuck, A new proof that analytic sets are Ramsey, Journal of Symbolic Logic 39 (1974), 163-165], and for each α<ω1,Rα+1 coming immediately after Rα in complexity. Associated with each Rα is an ultrafilter Uα, which is Ramsey for Rα, and in particular, is a rapid p-point satisfying certain partition properties. We prove Ramsey-classification theorems for equivalence relations on fronts on Rα,1≤α<ω1. These form a hierarchy of extensions of the Pudlak-Rödl Theorem canonizing equivalence relations on barriers on the Ellentuck space. We then apply our Ramsey-classification theorems to completely classify all Rudin-Keisler equivalence classes of ultrafilters which are Tukey reducible to Uα, for each 1≤α<ω1: Every nonprincipal ultrafilter which is Tukey reducible to Uα is isomorphic to a countable iteration of Fubini products of ultrafilters from among a fixed countable collection of rapid p-points. Moreover, we show that the Tukey types of nonprincipal ultrafilters Tukey reducible to Uα form a descending chain of rapid p-points of order type α+1.en
dc.publisherElsevier-
dc.relation.ispartofElectronic Notes in Discrete Mathematicsen
dc.subjectBarrier | Erdos-Rado Theorem | Pudlák-Rödl Theorem | Ramsey-classification theorem | Tukey types | Ultrafilteren
dc.titleA new class of Ramsey-Classification Theorems and their Applications in the Tukey Theory of Ultrafilters, Parts 1 and 2en
dc.typeArticleen
dc.identifier.doi10.1016/j.endm.2013.07.018en
dc.identifier.scopus2-s2.0-84883433401en
dc.relation.firstpage107en
dc.relation.lastpage112en
dc.relation.volume43en
item.openairetypeArticle-
item.openairecristypehttp://purl.org/coar/resource_type/c_18cf-
item.cerifentitytypePublications-
item.grantfulltextnone-
item.fulltextNo Fulltext-
crisitem.author.orcid0000-0003-4543-7962-
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