The Ordering Principle and Higher Dependent Choice

We provide, for any regular uncountable cardinal $\kappa$, a new argument for Pincus’ result on the consistency of $\mathrm{Z}\mathrm{F}$ with the higher dependent choice principle ${\mathrm{D}\mathrm{C}}_{<\kappa }$ and the ordering principle in the presence of a failure of the axiom of choice. We also generalise his methods and obtain these consistency results in a larger class of models.