 In what follows, the notation \(\vdash_{\mathcal{T}} \alpha\) is used to say that theory \(\mathcal{T}\) contains sentence \(\alpha\), and \(\Gamma \vdash_{\mathcal{T}} \alpha\) is used to say that \(\alpha\) follows from the premises collected in \(\Gamma\) according to \(\mathcal{T}\) (i.e., according to \(\mathcal{T}\)’s consequence relation  \(\vdash_{\mathcal{T}}\)).[3]  Except in  section 4.2.1,  however, we will be concerned only with claims about what follows according to the theory from a single premise, i.e., claims expressed by  sentences of form \(\gamma \vdash_{\mathcal{T}} \alpha\). (We rely on context to make clear  where such a sentence is being used and where it is only being mentioned.)