7
votes
2answers
204 views

Does forcing with recursively pointed perfect trees add a Turing degree that is minimal over $V$?

A tree $T$ on $\omega$ is recursively pointed if it is recursive in each of its branches. We can consider a variant of Sacks forcing where the conditions are recursively pointed perfect trees ordered ...
6
votes
2answers
464 views

Natural statements independent from true $\Pi^0_2$ sentences

I am looking for sentences in the language of first order arithmetic ($0,1,+,\cdot,\leq$) which are independent from $\Pi^0_2$ consequences of true arithmetic $\Pi^0_2\text{-}\mathsf{Th}(\mathbb{N})$. ...
5
votes
1answer
305 views

An eventually different function adding no Solovay real nor dominating function?

Definitions I believe set theorists have studied all of the following three notions in the context of forcing extensions of a model of ZFC, $M$ (hopefully the terminology is the standard one). A ...