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Combinatorial properties of infinite sets. This is a corner-point of set theory and combinatorics.

Infinite combinatorics deals with various combinatorial properties of infinite sets. The topics might include, for example,

• Ramsey theory on countably infinite sets, including results related to Szemerédi's theorem, Hindman's theorem, etc.
• Ramsey theory on uncountable sets, such as the Erdős–Rado theorem, and partition calculus
• Diamond ($$\diamondsuit$$) principles and relatives (such as $$\clubsuit$$), square ($$\Box$$) principles, club-guessing principles
• Combinatorial properties of infinite graphs or partial orders (such as their chromatic number, marriage problems, etc)
• Cardinal characteristic of the continuum and related topics
• Infinite trees, such as Kurepa trees or Aronszajn trees;
• Ramsey ultrafilters, p-points and related topics.
• (Maximal) almost disjoint families.

Closely related tags include . , and .