A partition theorem for scattered order types

A partition theorem for scattered ordered types was presented. It was shown that given a target element and a cardinal for the number of colours, there is another element of the class which, when coloured with required numbers, always has a monocoloured copy of the target. It was also shown that for every scattered order type.φ and cardinal μ there exists a scattered order type ψ such that ψ→[φ]_μ,ω¹ holds. It was also shown that for every scattered order type φ and natural number n, there is a scatteed order type ψ such that ψ→(φ) _n¹ holds.