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](https://en.wikipedia.org/wiki/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](https://en.wikipedia.org/wiki/Cardinal_characteristic_of_the_continuum) and related topics
* Infinite trees, such as [Kurepa trees](https://en.wikipedia.org/wiki/Kurepa_tree) or [Aronszajn trees](https://en.wikipedia.org/wiki/Aronszajn_tree);
* Ramsey ultrafilters, p-points and related topics.
* (Maximal) almost disjoint families.

Closely related tags include [tag:combinatorial-set-theory]. [tag:additive-combinatorics], and [tag:small-uncountable-cardinals].