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

Solved by gpt-5.6-sol high.

Solution

Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 144 / 3 / b / ii / Solution

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A complete type $p\in S_n(A)$ is isolated when some formula $\varphi\in p$ belongs to no other complete type in $S_n(A)$. Equivalently, the basic open set determined by $\varphi$ is the singleton $\{p\}$.


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 Incoming links: Isolated type