Turing degree
For any sets "X" and "Y", X join Y, written "X" ⊕ "Y", is defined to be the union of the sets } and }. The Turing degree of "X" ⊕ "Y" is the least upper bound of the degrees of "X" and "Y". Thus formula_1 is a join-semilattice. The least upper bound of degrees a and b is denoted a ∪ b. It is known that formula_1 is not a lattice, as there are pairs of degrees with no greatest lower bound.