Low basis theorem

The low basis theorem is one of several basis theorems in computability theory, each of which showing that, given an infinite subtree of the binary tree ${\displaystyle 2^{<\omega }}$, it is possible to find an infinite path through the tree with particular computability properties. The low basis theorem, in particular, shows that there must be a path which is low; that is, the Turing jump of the path is Turing equivalent to the halting problem ${\displaystyle \emptyset '}$.