Computably strongly self-absorbing C*-algebras

We introduce the notion of a computably strongly self-absorbing C*-algebra and show that the following C*-algebras are computably strongly self-absorbing: the Cuntz algebras ${\mathcal{O}}_2$ and ${\mathcal{O}}_{\mathrm{\infty }}$, the UHF algebra $M_{\mathfrak{n}}(\mathbb{C})$ and the tensor product $M_{\mathfrak{n}}(\mathbb{C})\otimes {\mathcal{O}}_{\mathrm{\infty }}$, where $\mathfrak{n}$ is a supernatural number of infinite type with computably enumerable support, and the Jiang-Su algebra $\mathcal{Z}$. In connection with the last example, we show that $\mathcal{Z}$ has a computable presentation. The results above are a special instance of a computable version of the standard approximate intertwining argument due to Elliott.