Recent work in reverse mathematics on combinatorial principles below Ramsey's theorem for pairs has made use of a variety of computable reductions to give a finer analysis of the relationships between these principles. We use three concrete examples to illustrate this work, survey the known results and give new negative results concerning RT_k~1, SRT_ℓ~2 and COH. Motivated by these examples, we introduce several variations of ADS and describe the relationships between these principles under Weihrauch and strong Weihrauch reductions.
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