The constructible universe 
is the class of sets
obtained by iterating definability along the ordinal
numbers. If 
denotes the subsets of 
definable over 
by first-order logic
formulas with parameters from 
, the constructible hierarchy is
 |  |  |
(1)
| ||
 |  |  |
(2)
| ||
 |  |  |  |  |
(3)
|
where 
is a limit ordinal. The constructible universe is
the proper class
 |
(4)
|
where 
is the class of all ordinal
numbers. The axiom of constructibility 
asserts that every set belongs to
(Müller and Sargsyan 2025).
