Using Ultrafilters to Prove Ramsey-type Theorems

DOI10.1080/00029890.2022.2004848OpenAlexW4205533240WikidataQ113853667 ScholiaQ113853667MaRDI QIDQ5037304

David J. Fernández Bretón

Publication date: 28 February 2022

Published in: The American Mathematical Monthly (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1711.01304

zbMATH Keywords

ultrafiltersvan der Waerden's theorem

Mathematics Subject Classification ID

Ramsey theory (05D10) Special constructions of topological spaces (spaces of ultrafilters, etc.) (54D80)

Cites Work

• Algebra in the Stone-Čech compactification. Theory and applications
• Semigroups in which all strongly summable ultrafilters are sparse
• Distral transformation groups
• The use of ultraproducts in commutative algebra
• Topological dynamics and combinatorial number theory
• Finite sums from sequences within cells of a partition of N
• A short proof of Hindman's theorem
• Nonstandard methods in Ramsey theory and combinatorial number theory
• Density and Ramsey type results on algebraic equations with restricted solution sets
• The elementary theory of finite fields
• Introduction to Ramsey Spaces (AM-174)
• Monochromatic Solutions to
• Diophantine Problems Over Local Fields I
• The Existence of Certain Ultrafilters on N and a Conjecture of Graham and Rothschild
• Ramsey's Theorem for n-Parameter Sets
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