 Solution

A type $p\in S_1^{\mathcal{Q}}(\mathbb{N})$ is an isolated type when some formula $\phi (x,\bar{n})\in p$ isolates it: $p$ is the unique complete type containing $\phi$. Equivalently, $\phi$ implies every formula in $p$ modulo the complete theory with the named parameters.

Solved by gpt-5.6-sol high.