@article{e7abf50f603542c3873fc77a8a54e526,
title = "Combinatorial principles equivalent to weak induction",
abstract = "We consider two combinatorial principles, ERT and ECT. Both are easily proved in RCA 0 plus ς 2 0 induction. We give two proofs of ERT in RCA 0 , using different methods to eliminate the use of ς 2 0 induction. Working in the weakened base system RCA 0 a-, we prove that ERT is equivalent to ς 1 0 induction and ECT is equivalent to ς 2 0 induction. We conclude with a Weihrauch analysis of the principles, showing ERT W LPO a-< W TC N a-W ECT. ",
keywords = "induction, Reverse mathematics, Weihrauch reduction",
author = "Caleb Davis and Hirschfeldt, {Denis R.} and Jeffry Hirst and Jake Pardo and Arno Pauly and Keita Yokoyama",
note = "Funding Information: Discussions contributing to this work occurred at the Workshop on Ramsey Theory and Computability, organized by Peter Cholak and held July 9–13 of 2018 at the Rome Notre Dame Global Gateway. Further discussions occurred at Dagstuhl Seminar 18361, organized by Vasco Brattka, Damir Dzhafarov, Alberto Marcone, and Arno Pauly, and held September 2–7 of 2018 at Schloss Dagstuhl, the Leibniz-Zentrum f{\"u}r Informatik. Denis Hirschfeldt was partially supported by grant DMS-1600543 from the National Science Foundation of the United States. Jeffry Hirst{\textquoteright}s travel was supported by a SAFE grant from the College of Arts and Sciences, a grant from the Office of International Education and Development, and a Board of Trustees travel grant, all from Appalachian State University. Yokoyama was partially supported by JSPS KAKENHI (grant numbers 19K03601 and 15H03634), JSPS Core-to-Core Program (A. Advanced Research Networks) and JAIST Research Grant 2018 (Houga). Publisher Copyright: {\textcopyright} 2020-IOS Press and the authors. All rights reserved.",
year = "2020",
doi = "10.3233/COM-180244",
language = "English",
volume = "9",
pages = "219--229",
journal = "Computability",
issn = "2211-3568",
publisher = "IOS Press",
number = "3-4",
}