Applications of Ramsey's Theorem

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SUMMARY

Ramsey's Theorem has significant applications beyond its traditional uses, including the construction of functions in natural numbers to verify properties of real number sequences and addressing propositions related to points in convex position, exemplified by the Erdős-Szekeres Problem. Additional applications span various fields of mathematics, such as combinatorics, graph theory, and topology. The theorem's implications are crucial for understanding complex structures and relationships within these domains.

PREREQUISITES
  • Understanding of combinatorial mathematics
  • Familiarity with graph theory concepts
  • Knowledge of convex geometry
  • Basic principles of mathematical logic
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Hey, Guys!

I wonder what applications of Ramsey's famous theorem there exist apart from such cases as:
1) constructions of functions in the domain of natural numbers to check some properties of sequences of real numbers.
2) propositions about points in convex postition (Erdos-Szekeres Problem)

I don't ask for detailed descriptions, although they are also welcome.
You can simply give a short sketch of applications in different fields of maths or give a link.

Thanks in advance! :smile:
 
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