Combinatorial principles equivalent to weak induction

Caleb Davis, Denis R. Hirschfeldt, Jeffry Hirst, Jake Pardo, Arno Pauly, Keita Yokoyama

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


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.

Original languageEnglish
Pages (from-to)219-229
Number of pages11
Issue number3-4
Publication statusPublished - 2020
Externally publishedYes


  • induction
  • Reverse mathematics
  • Weihrauch reduction

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science Applications
  • Computational Theory and Mathematics
  • Artificial Intelligence


Dive into the research topics of 'Combinatorial principles equivalent to weak induction'. Together they form a unique fingerprint.

Cite this