# Computable Reductions and Reverse Mathematics

Conference paper

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## Abstract

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 \(\mathsf {RT}^1_k\), \(\mathsf {SRT}^2_\ell \) and \(\mathsf {COH}\). Motivated by these examples, we introduce several variations of \(\mathsf {ADS}\) and describe the relationships between these principles under Weihrauch and strong Weihrauch reductions.

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© Springer International Publishing Switzerland 2016