Re: The set of necessary FISONs

On 28.02.2025 01:00, Jim Burns wrote:

On 2/27/2025 5:01 PM, WM wrote:

Zermelo's approach does not extend ∀n:Aᴺ(n) to Aᴺ(ℕ)

It does. Zermelo says it, and it is easy to prove it:
Adding all natural numbers established the set ℕ.

Zermello's Infinity guarantees a superset Z of Z₀

>
How is that accomplished?

 By Zermelo's approach:
Z ⇒ 𝒫(Z)

How is Z accomplished?

It's not.even.wrong.
 And it's not Zermelo's approach,
Z

Where does he get is Z from?

His Z is ensured by induction.

 Nope.

{ } and a ==> {a}.

We don't even need the intersection
if we reduce Zermelo's approach to
Lorenzen's approach:
I is a natural number, and
if x is a natural numbers then x+1 is a natural number.

 Consider Robinson arithmetic.

No.

Proofs by induction are unreliable in Robinson arithmetic.

Irrelevant.

 Wherever you got Lorenzen's approach from,
send it back.

Then you admit to stand outside of mathematics. Lorenzen uses the same induction as Cantor, Dedekind, Peano, Schmidt, Zermelo, or v. Neumann.
Addition of all natnumbers results in the set of all natnumbers.
Regards, WM