A new class of Ramsey-classification theorems and their applications in the Tukey theory of ultrafilters, Part 2

DOI10.1090/S0002-9947-2014-06122-9zbMath1311.05202arXiv1205.5909OpenAlexW1966654800MaRDI QIDQ5247014

Natasha Dobrinen, Stevo Todorčević

Publication date: 22 April 2015

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1205.5909

zbMATH Keywords

Pudlak-Rödl theoremTukey classification problem

Mathematics Subject Classification ID

Partial orders, general (06A06) Ramsey theory (05D10) Other combinatorial set theory (03E05) Special constructions of topological spaces (spaces of ultrafilters, etc.) (54D80) Partition relations (03E02) Ordered sets and their cofinalities; pcf theory (03E04)

Related Items (21)

Spectra of Tukey types of ultrafilters on Boolean algebras ⋮ Creature forcing and topological Ramsey spaces ⋮ Tukey types of ultrafilters ⋮ A long chain of P-points ⋮ Ideals and their generic ultrafilters ⋮ Topological Ramsey spaces from Fraïssé classes, Ramsey-classification theorems, and initial structures in the Tukey types of \(p\)-points ⋮ Ramsey for R1 ultrafilter mappings and their Dedekind cuts ⋮ Selective ultrafilters on FIN ⋮ Cofinal types on ω₂ ⋮ Local Ramsey theory: an abstract approach ⋮ Preserved under Sacks forcing again? ⋮ On embedding certain partial orders into the P-points under Rudin-Keisler and Tukey reducibility ⋮ Continuous and other finitely generated canonical cofinal maps on ultrafilters ⋮ Topological Ramsey spaces and metrically Baire sets ⋮ A new class of Ramsey-classification theorems and their application in the Tukey theory of ultrafilters, Part 1 ⋮ Banach Spaces from Barriers in High Dimensional Ellentuck Spaces ⋮ Triangular Ramsey Numbers ⋮ CLASSES OF BARREN EXTENSIONS ⋮ Ramsey degrees of ultrafilters, pseudointersection numbers, and the tools of topological Ramsey spaces ⋮ Parametrizing by the Ellentuck space ⋮ Selective but not Ramsey

Cites Work

• Tukey types of ultrafilters
• Cofinal types of ultrafilters
• Partition theorems for systems of finite subsets of integers
• Forcing with filters and complete combinatorics
• Topological Ramsey spaces from Fraïssé classes, Ramsey-classification theorems, and initial structures in the Tukey types of \(p\)-points
• Fraïssé limits, Ramsey theory, and topological dynamics of automorphism groups
• HIGH DIMENSIONAL ELLENTUCK SPACES AND INITIAL CHAINS IN THE TUKEY STRUCTURE OF NON-P-POINTS
• Introduction to Ramsey Spaces (AM-174)
• A new proof that analytic sets are Ramsey
• Ultrafilter Mappings and Their Dedekind Cuts
• A notion of selective ultrafilter corresponding to topological Ramsey spaces
• A new class of Ramsey-classification theorems and their application in the Tukey theory of ultrafilters, Part 1
• The Rudin-Keisler Ordering of P-Points
• A Combinatorial Theorem

This page was built for publication: A new class of Ramsey-classification theorems and their applications in the Tukey theory of ultrafilters, Part 2