Generic existence of ultrafilters on the natural numbers

DOI10.4064/fm730-5-2016zbMath1420.03119OpenAlexW2551721738MaRDI QIDQ2957271

Jana Flaskova, Jörg Brendle

Publication date: 25 January 2017

Published in: Fundamenta Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4064/fm730-5-2016

zbMATH Keywords

Ramsey ultrafilterultrafilterP-pointsummable idealcardinal invariant of the continuumgeneric existencedensity zero ideal

Mathematics Subject Classification ID

Descriptive set theory (03E15) Consistency and independence results (03E35) Continuum hypothesis and Martin's axiom (03E50) Cardinal characteristics of the continuum (03E17)

Related Items (17)

Every maximal ideal may be Katětov above of all 𝐹_{𝜎} ideals ⋮ Characterizing existence of certain ultrafilters ⋮ Indestructibility of ideals and MAD families ⋮ Katětov order on Borel ideals ⋮ On Pospíšil ideals ⋮ WAYS OF DESTRUCTION ⋮ Ideal approach to convergence in functional spaces ⋮ HL ideals and Sacks indestructible ultrafilters ⋮ Generic existence of interval P-points ⋮ On P-like ideals induced by disjoint families ⋮ PARTITION FORCING AND INDEPENDENT FAMILIES ⋮ Michael spaces and ultrafilters ⋮ The relationship between \(\mathcal{D}_{f i n} \)-ultrafilter and \(Q\)-point ⋮ Pseudointersection numbers, ideal slaloms, topological spaces, and cardinal inequalities ⋮ Relations between the \({\mathcal {I}}\)-ultrafilters ⋮ TOWERS IN FILTERS, CARDINAL INVARIANTS, AND LUZIN TYPE FAMILIES ⋮ More on MAD families and \(P\)-points

Cites Work

• There may be simple \(P_{\aleph _ 1}\)- and \(P_{\aleph _ 2}\)-points and the Rudin-Keisler ordering may be downward directed
• Ultrafilters with small generating sets
• Pair-splitting, pair-reaping and cardinal invariants ofFσ-ideals
• Strong measure zero sets without Cohen reals

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