 To build a classical model for \(\mathcal{L}^{+}_0\), we need an extension for \(\Tr\). Let us pick a set: call it \(H\) for a hypothesis about what the extension of \(\Tr\) might be. \(H\) may be \(\varnothing\), it may be the entire domain of \(\mathcal{M}_0\), or it may be anything else. It need not be a particularly good approximation of the semantic properties of \(\Tr\).