Some arithmetic Ramsey theoretic results via ultrafilters and the Stone-Cech compactification

Date

2026-7-20

Author

Duman, Necdet

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In this thesis, with the goal of illustrating how ultrafilter techniques are used to prove results in arithmetic Ramsey theory, we survey two recent results. After providing the necessary background regarding ultrafilters and the algebra of the Stone-Cech compactification of a discrete semigroup, we first present the proof of Hindman's conjecture for two colors given by Bowen and then present a result by by Di Nasso and Ragosta that can be considered as an infinitary exponential version of Schur's theorem.

Subject Keywords

Ultrafilters, Stone–Čech Compactification, Ramsey Theory

URI

https://hdl.handle.net/11511/119945

Collections

Graduate School of Natural and Applied Sciences, Thesis