limitation of working with first order logic as discussed in Section \[FOL\] could potentially undermine a full implementation of a hyperreal scheme for Leibnizian infinitesimal calculus.

With this in mind, let us consider Skolem’s construction of nonstandard natural numbers [@Sk33], [@Sk34], [@Sk55]; see [@KKM section 3.2] for additional references. It turns out that one needs many, many nonstandard numbers in order to move from $\mathbb{N}$ to ${}^\ast\mathbb{N}$, e.g., in Henkin’s countable model one has $$\label{21}
{}^\ast\mathbb{N}=\mathbb{N} + (\mathbb{Z}\times\mathbb{Q}).$$ Here we use ${{\mathbb Q}}$ to indicate that the galaxies are dense, so that between any pair of galaxies there is another galaxy (a galaxy is the set of numbers at finite distance from each other). Meanwhile ${{\mathbb Z}}$ indicates that each galaxy other than the original ${{\mathbb N}}$ itself is order-isomorphic to ${{\mathbb Z}}$ rather than to ${{\mathbb N}}$, because for each infinite $H$ the number $H-1$ is in the same galaxy.

Leibniz arguably did not have such a perspective. In other words, one needs to build up a considerable conceptual machinery to emulate Leibniz’s probably rather modest arsenal of procedural moves. That is to say, we may be able to emulate all of Leibniz moves in a modern B-framework, such 