Re: Peano's second axiom.

On Jun 30, 4:36 am, Zaljo...@xxxxxxxxx wrote:
On Jun 29, 6:43 pm, MoeBlee <jazzm...@xxxxxxxxxxx> wrote:

On Jun 29, 5:16 pm, Zaljo...@xxxxxxxxx wrote:

Ax( x is a number -> Ey( y=S(x) ) ).

Second point: Even with theory with a predicate 'is a number', what
you want to say is as simple as:

An(n is a number -> Sn is a number)

We don't need

Ey y = Sn

since it is already a theorem of first order identity theory.

Yes, actually that's what I wanted to know. But how do you prove this
theorem?

Easy:

1. Sn = Sn
2. Ey y = Sn by EI in 1.

Are you sure this is what you wanted to know?

Regards

.