Logic Workshop

March 8
Rose Weisshaar, Universty of Pennsylvania
Mathias generics over a countable Turing ideal

We consider effective Mathias forcing over a countable Turing ideal. In particular, we show that a Mathias generic constructed with conditions from a countable ideal $\mathcal{I}$ need not compute a Mathias generic over every smaller ideal $\mathcal{J} \subseteq \mathcal{I}$, answering a question of Cholak, Dzhafarov, and Soskova. This is joint work with Henry Towsner and Dan Turetsky.