Computable Reductions and Reverse Mathematics

  • Reed Solomon
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9709)


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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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.University of ConnecticutStorrsUSA

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