Semantic consequence of contradictions Does a contradiction entail any arbitrary formula?
If $\varphi$ is a contradiction, then $\varphi \rightarrow \psi$ is a tautology and therefore $\varphi \models \psi$ is true as well no matter what $\psi$ is, right?

Yes, that is correct, we say $\phi \models  \psi$, if for all interpretations such that $\phi$ is true, $\psi$ is true, but since in your case $\phi$ is a contradiction, there are no interpretations for which $\phi$ is true, so (vacuously) we have $\phi \models  \psi$, for any $\psi$.
