Conservation theorems for the Cohesiveness Principle

David R. Belanger

We prove that the Cohesiveness Principle (COH) is ${\Pi }_1^1$ conservative over $RC{A}_0+I{\Sigma }_n^0$ and over $RC{A}_0+B{\Sigma }_n^0$ for all $n\ge 2$ by recursion-theoretic means. We first cha…