Note, however, that such theorists are typically careful to avoid explicitly asserting that there are only finitely many feasible numbers. Instead they give examples of expressions whose denotations (were they to exist) would be infeasibly large – e.g. those given in the formulation of (S2). Certainly the claim that there is a largest feasibly constructible number would invite the challenge that the strict finitist nominate such a number \(n\). And any such nomination would in turn invite the rejoinder that if \(n\) is feasibly constructible, then \(n+1\) must be as well. But in the sort of model \(\mathcal{M}\) under consideration the definite description ‘the largest \(x\) such that \(2^x\) exists’ will be non-denoting in virtue of the fact that the elements \(n \in \mathcal{M}\) such that \(\mathcal{M} \models \exists z \varepsilon(2,n,z)\) form a proper initial segment. The existence of such models might thus be taken to elucidate Yessenin-Volpin’s (1970) claim that there are distinct natural number sequences which are distinguished by the primitive recursive functions under which they are closed.[55]