Ideal version of Ramsey’s theorem

DOI10.1007/s10587-011-0073-3zbMath1249.05378OpenAlexW2077618423MaRDI QIDQ3118019

Nikodem Mrożek, Ireneusz Recław, Rafał Filipów, Piotr Szuca

Publication date: 1 March 2012

Published in: Czechoslovak Mathematical Journal (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/10338.dmlcz/141533

zbMATH Keywords

statistical convergenceRamsey's theoremideal convergencemonotone sequencesubsequenceBolzano-Weierstrass propertystatistical densityBolzano-Weierstrass theoremideal of subsets of natural numbers

Mathematics Subject Classification ID

Combinatorial aspects of partitions of integers (05A17) Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.) (54A20) Density, gaps, topology (11B05) Ramsey theory (05D10) Ideal and statistical convergence (40A35)

Related Items (10)

The Borel complexity of ideal limit points ⋮ Ramsey type properties of ideals ⋮ Achievement sets and sum ranges with ideal supports ⋮ Filter-dependent versions of the uniform boundedness principle ⋮ Selective separability on spaces with an analytic topology ⋮ On the structure of Borel ideals in-between the ideals \(\mathcal{ED}\) and fin \(\otimes\) fin in the Katětov order ⋮ Ideal versions of the Bolzano-Weierstrass property ⋮ Mad families, P+(I)-ideals and ideal convergence ⋮ A note on a new ideal ⋮ On the Mikusiński-Antosik diagonal theorem and the equivalence of two types of convergence in Köthe spaces

Cites Work

• Unnamed Item
• Topics in topology
• Monotonicity
• Density versions of Schur's theorem for ideals generated by submeasures
• Superfilters, Ramsey theory, and van der Waerden's theorem
• Proper forcing
• Analytic ideals and their applications
• Iterated combinatorial density theorems
• Van der Waerden spaces
• Semiselective coideals
• Analytic quotients: theory of liftings for quotients over analytic ideals on the integers
• Ideal convergence of bounded sequences
• Ultrafilters on a countable set

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