 This theory can be made stronger by indicating how to pass to transfinite typed approximations. The type \(\alpha + 1\) approximation to a set will always be the set of type \(\alpha\) approximations; if \(\lambda\) is a limit ordinal, the type \(\lambda\) approximation will be the sequence \(\{s_{\beta} \}_{\beta \lt \lambda}\) of approximants to the set at earlier levels (so our “intended model” above is the set of type \(\omega\) approximations in a larger model).