### Single Idea 10686

#### [catalogued under 4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX]

Full Idea

We cannot explicitly define one-one correspondence from the sets to the ordinals (because there is no explicit well-ordering of R). Nevertheless, the Axiom of Choice guarantees that a one-one correspondence does exist, even if we cannot define it.

Clarification

'R' is the real numbers

Gist of Idea

The Axiom of Choice guarantees a one-one correspondence from sets to ordinals

Source

Keith Hossack (Plurals and Complexes [2000], 10)

Book Reference

-: 'British Soc for the Philosophy of Science' [-], p.436