The Sacks density theorem and Σ2-bounding
Marcia J. Groszek, Michael E. Mytilinaios, Theodore A. Slaman · Journal of Symbolic Logic · 1996
Abstract The Sacks Density Theorem [7] states that the Turing degrees of the recursively enumerable sets are dense. We show that the Density Theorem holds in every model of P− + BΣ2. The proof has two components: a lemma that in any model of P− + BΣ2, if B is recursively enumerable and incomplete then IΣ1 holds relative to B and an adaptation of Shore's [9] blocking technique in α-recursion theory to models of arithmetic.