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We will show that separable unital AF-algebras whose Bratteli diagrams do notallow converging two nodes into one node, can be classified up to the tensorproduct with the universal UHF-algebra $\Q$ only by their trace spaces. Thatis, if $\A$ and $\B$ are such AF-algebras, then $T(A)=T(B)$ if and only if$\A\otimes \Q \cong \B\otimes \Q$.

A class of AF-algebras up to universal UHF-algebra stability