Full Idea
For the reduction of Peano Arithmetic to ZF set theory, usually the set of finite von Neumann ordinals is used to represent the non-negative integers.
Gist of Idea
To reduce PA to ZF, we represent the non-negative integers with von Neumann ordinals
Source
Volker Halbach (Axiomatic Theories of Truth [2011], 6)
Book Reference
Halbach,Volker: 'Axiomatic Theories of Truth' [CUP 2011], p.41
A Reaction
Halbach makes it clear that this is just one mode of reduction, relative interpretability.
Related Ideas
Idea 15925 Each Von Neumann ordinal number is the set of its predecessors [Neumann, by Lavine]
Idea 10997 Von Neumann numbers are helpful, but don't correctly describe numbers [Read]