Nonstandard analysis reduces to just the Compactness Theorem of First-Order Logic. One happy consequence of this is that it's compatible with classical logic, u

Nonstandard analysis reduces to just the Compactness Theorem of First-Order Logic. One happy consequence of this is that it's compatible with classical logic, unlike SIA/SDG. The seemingly very intuitive arguments in Bell's book "a primer of infinitesimal analysis" are only heuristics. It's also disturbing how the nilsquare "infinitesimals" in SIA/SDG satisfy δ^2 = ε^2 = 0 but NOT necessarily εδ = 0! By contrast, you can more easily obtain nilpotent infinitesimals by using NSA and combining it with little-o notation (on hyperreal numbers, and NOT on functions and their asymptotic growth rates). Then the geometric arguments in Bell's "a primer of infinitesimal analysis" can still be carried out, but are more easy to unravel back to core definitions.