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2016 | OriginalPaper | Chapter

Computable Reductions and Reverse Mathematics

Author : Reed Solomon

Published in: Pursuit of the Universal

Publisher: Springer International Publishing

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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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previous chapter AFCAL and the Emergence of Computer Science in France: 1957–1967
next chapter Busy Beavers and Kolmogorov Complexity
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Astor, E.P., Dzhafarov, D.D., Solomon, R., Suggs, J.: The uniform content of partial and linear orders (in preparation)
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Metadata
Title
Computable Reductions and Reverse Mathematics
Author
Reed Solomon
Copyright Year
2016
Book
Pursuit of the Universal

Print ISBN: 978-3-319-40188-1

Electronic ISBN: 978-3-319-40189-8

Copyright Year: 2016

DOI
https://doi.org/10.1007/978-3-319-40189-8_19

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