Nonprincipal partial type
= Nonprincipal partial type
A <partial type> is nonprincipal when it is not a <principal partial type>. Equivalently, for every formula $\theta(\mathbf x)$ consistent with $T$, some $\psi\in p$ makes $\theta\land\neg\psi$ consistent with $T$. This is the exact extension property needed in the <Henkin construction> proving the <omitting types theorem>.