The finite cohesiveness principle

We investigate the logical strength of the cohesiveness principle when restricted to finite sequences of sets, denoted by fin-COH, over different base theories. Our main result shows that fin-COH entails $I{\mathrm{\Sigma }}_1^0$ over the weaker base theory $RC{A}_0^{\ast }$, thereby answering a question posed by Fiori-Carones, Kołodziejczyk and Kowalik. In addition, we show that fin-COH is not provable over $WK{L}_0$.