Σ1-Collection and the finite injury priority method
We show that there is an intermediate recursively enumerable Turing degree in every model of P−+BΣ1. The proof is not uniform, depending on whether IΣ1 holds. There is a model of P−+BΣ1 in which there is a least recursively enumerable degree strictly above the recursive degree. Thus, the Sacks Splitting Theorem cannot be proven in P−+BΣ1.
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