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 .