In this paper, we give a characterization of the strong degrees of categoricity of computable structures greater or equal to $0^{″}$. They are precisely the treeable degrees — the least degrees of paths through computable trees — that compute $0^{″}$. As a corollary, we obtain several new examples of degrees of categoricity. Among them we show that every degree $d$ with $0^{(\alpha )}\le d\le 0^{(\alpha +1)}$ for $\alpha$ a computable ordinal greater than $2$ is the strong degree of categoricity of a rigid structure. Using quite different techniques we show that every degree $d$ with $0^{\prime }\le d\le 0^{″}$ is the strong degree of categoricity of a structure. Together with the above example this answers a question of Csima and Ng. To complete the picture we show that there is a degree $d$ with $0^{\prime }<d<0^{″}$ that is not the degree of categoricity of a rigid structure.

在本文中，我们给出了可计算结构的强范畴度的表征，大于或等于$0^{”}$。它们正是可树度——通过可计算树的路径的最小度——计算$0^{”}$。作为推论，我们获得了几个新的类别度示例。其中我们表明每个度$d$和$0^{(\alpha ）}\le d\le 0^{(\alpha +1）}$为了$\alpha$可计算序数大于$2$是刚性结构的强范畴化程度。使用完全不同的技术，我们表明每个学位$d$和$0^{\prime }\le d\le 0^{”}$是结构的强范畴化程度。结合上面的例子，这就回答了 Csima 和 Ng 的问题。为了完成图片，我们表明有一个学位$d$和$0^{\prime }<d<0^{”}$这不是刚性结构的范畴化程度。