The cohesive and stable Ramsey theorems and proof size over a weak base theory

Leszek Aleksander Kołodziejczyk, Mengzhou Sun

We show that over the weak base theory ${\mathrm{RCA}}_0^{\ast }$, cohesive Ramsey's theorem for pairs ${\mathrm{CRT}}_2^2$ implies exponential closure of the definable cut ${\mathrm{I}}_1^0$,…