Re: The set of necessary FISONs

On 22.02.2025 13:13, FromTheRafters wrote:

WM formulated on Saturday :

On 22.02.2025 12:14, FromTheRafters wrote:

WM explained on 2/22/2025 :

On 22.02.2025 02:05, Richard Damon wrote:

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Note, as I understand it, that initial Zermelo Set Theory didn't even HAVE "induction",

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You don't understand it.

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He understands it better than you do apparently. Zermelo's theory didn't have transfinite induction.

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Who claimed that?

 Certainly not you.

Only stupids could do so.

First element and the successor function is induction.
 First element and successor function is 'inductive hypothesis' not induction.

Nonsense. The inductive step is proved in my example from |ℕ \ {1, 2, 3, ..., n}| = ℵo, i.e., by several axioms, and in Zermelo's example by a single axiom.
Regards, WM