  We will show that separable unital AF-algebras whose Bratteli diagrams do not
allow converging two nodes into one node, can be classified up to the tensor
product with the universal UHF-algebra $\Q$ only by their trace spaces. That
is, if $\A$ and $\B$ are such AF-algebras, then $T(A)=T(B)$ if and only if
$\A\otimes \Q \cong \B\otimes \Q$.
