François G. Dorais

Research in Logic and Foundations of Mathematics

Comparing the strength of diagonally non-recursive functions in the absence of $\Sigma^0_2$ induction

By F. G. Dorais, J. L. Hirst and P. Shafer
Journal of Symbolic Logic 80 (2015), no. 4, 1211–1235

We prove that the statement “there is a such that for every there is a -bounded diagonally non-recursive function relative to 4$f\mathrm{RCA}_0 + \mathrm{B}\Sigma^0_2k2\mathrm{I}\Sigma^0_2$$.