When a model is said to contain all the ordinals, what precisely does this mean? That is, what would an axiom (axioms) look like in order to insure that a model (or, more strictly, its universe) contains all the ordinals?
When a model is said to contain all the ordinals, what precisely does this mean? That is, what would an axiom (axioms) look like in order to insure that a model (or, more strictly, its universe) contains all the ordinals?