# Example of a formal system that is complete but not strongly complete

A formal system is complete with respect to a semantics, if all validities are derivable (i.e. if $\ \vDash\phi\$ then $\ \vdash\phi$).

A formal system is strongly complete with respect to a semantics, if for every set of formulas $\Gamma$, the formulas that are semantically entailed by $\Gamma$ are derivable from $\Gamma$ (i.e. if $\ \Gamma\vDash\phi\$ then $\ \Gamma\vdash\phi$).

What is an example of a formal system that is complete wrt a semantics but not strongly complete wrt to that semantics?