more from Volker Halbach

Single Idea 16312

[catalogued under 6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory]

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


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]