In mathematics, structural Ramsey theory is a categorical generalisation of Ramsey theory, rooted in the idea that many important results of Ramsey theory have "similar" logical structures. The key observation is noting that these Ramsey-type theorems can be expressed as the assertion that a certain category (or class of finite structures) has the Ramsey property (defined below).
Structural Ramsey theory began in the 1970s[1] with the work of Nešetřil and Rödl, and is intimately connected to Fraïssé theory. It received some renewed interest in the mid-2000s due to the discovery of the Kechris–Pestov–Todorčević correspondence, which connected structural Ramsey theory to topological dynamics.
^Van Thé, Lionel Nguyen (2014-12-10). "A survey on structural Ramsey theory and topological dynamics with the Kechris–Pestov–Todorcevic correspondence in mind". arXiv:1412.3254 [math.CO].
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