Ramsey regions

Ramsey regions

Let (T1, T2, . . . , Tc) be a fixed c-tuple of sets of graphs (i.e. each Ti is a set of graphs). Let R(c, n, (T1, T2, . . . , Tc)) denote the set of all n-tuples, (a1, a2, . . . , an), such that every c-coloring of the edges of the complete multipartite graph, Ka1,a2,...,an , forces a monochromatic subgraph of color i from the set Ti (for at least one i). If N denotes the set of non-negative in...

Ramsey on Truth and Truth on Ramsey

It is widely held, to the point of being the received interpretation, that Frank Ramsey was the first to defend the so-called Redundancy Theory of Truth in his landmark article ‘Facts and Propositions’ (hereafter ‘FP’) of 1927. For instance, A.J. Ayer cited this article in the context of arguing that saying that p is true is simply a way of asserting p and that truth is not a real quality or re...

Ramsey Theory

Induced Ramsey

Ramsey Theory

Ramsey Theory is the study of inevitable substructures in large (usually discrete) objects. For example, consider colouring the edges of the complete graph Kn with two colours. In 1930, Ramsey [13] proved that if n is large enough, then we can find either a red complete subgraph on k vertices or a blue complete subgraph on ` vertices. We write Rpk, `q for the smallest such n. Another famous exa...