Editing Countable set (section)

==Minimal model of set theory is countable==
If there is a set that is a standard model (see [[inner model]]) of ZFC set theory, then there is a minimal standard model (see [[Constructible universe]]). The [[Löwenheim–Skolem theorem]] can be used to show that this minimal model is countable. The fact that the notion of "uncountability" makes sense even in this model, and in particular that this model ''M'' contains elements that are:
* subsets of ''M'', hence countable,
* but uncountable from the point of view of ''M'',
was seen as paradoxical in the early days of set theory; see [[Skolem's paradox]] for more.

The minimal standard model includes all the [[algebraic number]]s and all effectively computable [[transcendental number]]s, as well as many other kinds of numbers.