Forcing with filters and complete combinatorics

DOI10.1016/0168-0072(89)90052-3zbMath0681.03035OpenAlexW1977280732MaRDI QIDQ1823241

Claude Laflamme

Publication date: 1989

Published in: Annals of Pure and Applied Logic (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0168-0072(89)90052-3

zbMATH Keywords

combinatoricspartial ordersultrafilterslinear order

Mathematics Subject Classification ID

Other combinatorial set theory (03E05) Other aspects of forcing and Boolean-valued models (03E40)

Related Items (34)

GAMES AND HEREDITARY BAIRENESS IN HYPERSPACES AND SPACES OF PROBABILITY MEASURES ⋮ 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 ⋮ Filters on a countable vector space ⋮ A simple \(P_{\aleph_1}\)-point and a simple \(P_{\aleph_2}\)-point ⋮ Local Ramsey theory: an abstract approach ⋮ Coideals as remainders of groups distinguishing between combinatorial covering properties ⋮ Preserved under Sacks forcing again? ⋮ A few special ordinal ultrafilters ⋮ Adding ultrafilters by definable quotients ⋮ A new class of Ramsey-classification theorems and their application in the Tukey theory of ultrafilters, Part 1 ⋮ Three orderings on \(\beta(\omega)\setminus\omega\) ⋮ The $\gamma _p$ property and the reals ⋮ The Menger property on \(C_p(X, 2)\) ⋮ Zapping Small Filters ⋮ Base tree property ⋮ Terminal notions in set theory ⋮ Terminal Notions ⋮ MATHIAS FORCING AND COMBINATORIAL COVERING PROPERTIES OF FILTERS ⋮ A local Ramsey theory for block sequences ⋮ Triangular Ramsey Numbers ⋮ The ultrafilter and almost disjointness numbers ⋮ Mathias and set theory ⋮ Fraïssé structures and a conjecture of Furstenberg ⋮ Luzin gaps ⋮ On strong $P$-points ⋮ Chains of P-points ⋮ The Rudin-Blass ordering of ultrafilters ⋮ CLASSES OF BARREN EXTENSIONS ⋮ A new class of Ramsey-classification theorems and their applications in the Tukey theory of ultrafilters, Part 2 ⋮ Ramsey degrees of ultrafilters, pseudointersection numbers, and the tools of topological Ramsey spaces ⋮ Selective but not Ramsey

Cites Work

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• Selctive ultrafilters and homogeneity
• Set theory. An introduction to independence proofs
• Compacts de fonctions mesurables et filtres non mesurables
• Some initial segments of the Rudin-Keisler ordering
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• Ultrafilter Mappings and Their Dedekind Cuts
• On the existence of P-points in the Stone-Čech compactification of integers
• Some points in βN
• Happy families
• Partition Theorems and Ultrafilters
• Ultrafilters on a countable set
• The Rudin-Keisler Ordering of P-Points

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