  In this series of papers, we advance Ramsey theory of colorings over
partitions. In this part, a correspondence between anti-Ramsey properties of
partitions and chain conditions of the natural forcing notions that homogenize
colorings over them is uncovered. At the level of the first uncountable
cardinal this gives rise to a duality theorem under Martin's Axiom: a function
$p:[\omega_1]^2\rightarrow\omega$ witnesses a weak negative Ramsey relation
when $p$ plays the role of a coloring if and only if a positive Ramsey relation
holds over $p$ when $p$ plays the role of a partition.
  The consistency of positive Ramsey relations over partitions does not stop at
the first uncountable cardinal: it is established that at any prescribed
uncountable cardinal these relations follow from forcing axioms without large
cardinal strength. This result solves in particular two problems from [CKS21].
