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

Ramsey theory over partitions I: Positive Ramsey relations from forcing axioms