The asymptotics of r(4,t)

For integers s, t 2, the Ramsey number r (s, t) denotes the minimum n such that every n-vertex graph contains a clique of order s or an independent set of order t. In this paper we prove \ r (4, t) = (t³log⁴ t) as\ t, \ which determines r (4, t) up to a factor of order log² t, and solves a conjecture of Erdős.