The second states that if a set of sentences in a countable first-order language has an infinite model, then there exists a model of arbitarily large cardinality. An order type effectively describes the properties of an ordinal. Alternatively an ordinal is a set with the special property that each element is the set of all its predecessors. The set of Rational numbers. The set of Real numbers.
Transitive sets form the basis for the construction of the ordinals .
Please note that V is not a set - it is a proper class. V can be defined in terms of the rank of a set. The set of Integers.