ZFC	Zermelo–Fraenkel set theory with the axiom of choice.
$\mathcal{B}$; $\mathbb{B}$	the smooth Basel topos; the site for $\mathcal{B}$.
B	the atomless random Boolean algebra.
$\mathcal{N}$; ${}^{*}N$; $\mathbb{N}$	the object of smooth N.N; nonstandard N.N.; the standard set of N.N.
Set	the category of sets and mappings.