$IP(G_0)$: the special isomorphism problem for $G_0$, i.e. Given $G_0$, determine if $G$ is isomorphic to $G_0$. My question is that how can we deduce from the Adian-Rabin theorem that $IP(G_0)$ is unsolvable for any finitely presented $G_0$? I have found the following paper:

https://projecteuclid.org/journals/bulletin-of-the-american-mathematical-society-new-series/volume-6/issue-1/The-word-problem-and-the-isomorphism-problem-for-groups/bams/1183548590.full

Is it true to say that Theorem 5, page 53 is derived from the Adian-Rabin Theorem? And if no, do you know a reference including the deduction of unsolvability of $IP(G_0)$ from the Adian-Rabin Theorem?

Thank you for your help.

$\operatorname{IP}(G_0)$: the special isomorphism problem for $G_0$, i.e., given $G_0$, determine if $G$ is isomorphic to $G_0$. My question is that how can we deduce from the Adian–Rabin theorem that $\operatorname{IP}(G_0)$ is unsolvable for any finitely presented $G_0$? I have found the following paper:

Stillwell - The word problem and the isomorphism problem for groups

Is it true to say that Theorem 5, page 53 is derived from the Adian–Rabin Theorem? And if no, do you know a reference including the deduction of unsolvability of $\operatorname{IP}(G_0)$ from the Adian–Rabin Theorem?