Re: The set of necessary FISONs

On 02.03.2025 13:22, Richard Damon wrote:

On 3/1/25 1:09 PM, WM wrote:

On 01.03.2025 17:25, Richard Damon wrote:

On 3/1/25 9:31 AM, WM wrote:

On 28.02.2025 20:45, Richard Damon wrote:

On 2/28/25 11:44 AM, WM wrote:

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No, Zermelo uses induction. I did not say that he uses the term induction.

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No, what you describe is NOT "induction".

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Correct your qualifiers. Or look it up.
F(1) ∈ F and F(n) ∈ F ==> F(n+1) ∈ F describes the infinite inductive set F of FISONs.

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You have a source that uses the term "Induction" for the recursive iteration that builds the set?

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∀P(P(0) /\ ∀k(P(k) ==> P(k+1)) ==> ∀n (P(n)))
Wikipedia

Induction is the nucleus: P(0) /\ ∀k(P(k) ==> P(k+1)

 And what SET did that build? P was a statement about a relationship.

P gives a relationship, for instance "is element of F". The universal quantifier ∀ proves that all FISONs belong to the set that can be removed.

You can try to claim that the system it creates is inconsistent, but to do so you need to show the error using the system as defined.

I did: UF = ℕ ==> Ø = ℕ.
Regards, WM