Summary: We further develop the theory of layered semigroups, as introduced by I. Farah et al. [J. Comb. Theory, Ser. A 98, No. 2, 268–311 (2002; Zbl 0991.05100)], providing a general framework to prove Ramsey statements about such a semigroup \(S\). By nonstandard and topological arguments, we show Ramsey statements on \(S\) are implied by the existence of coherent sequences in \(S\). This framework allows us to formalise and prove many results in Ramsey theory, including Gowers’ \( \text{FIN}_k\) theorem, the Graham-Rothschild theorem, and Hindman’s finite sums theorem. Other highlights include: a simple nonstandard proof of the Graham-Rothschild theorem for strong variable words; a nonstandard proof of Bergelson-Blass-Hindman’s partition theorem for located variable words, using a result of T. J. Carlson et al. [Trans. Am. Math. Soc. 358, No. 7, 3239–3262 (2006; Zbl 1083.05039)]; and a common generalisation of the latter result and Gowers’ theorem, which can be proven in our framework.