Re: The set of necessary FISONs

On 2/21/25 12:32 PM, WM wrote:

On 21.02.2025 13:18, Richard Damon wrote:

On 2/21/25 4:39 AM, WM wrote:

On 21.02.2025 02:18, Richard Damon wrote:
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In order to secure the existance of "infinite" sets, we still need the following axioms.

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Almost correct, but only singular: we still need the following axiom.

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Read what you wrote:
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  Axioms.

 You wrote it.
 

There is no mention of "induction" in the statement.

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The following axiom is the axiom of induction. The set Z contains the empty set as an element and with every element a also the element {a}.

 

I will admit that I haven't read the paper in the German, but I have studied the general concepts of the theory, and "induction" is not the basis of the existance of the infinite set, at least not in the final works.

 Either you have not understood the final works or they are irrelevant.
 Regards, WM
 

Since that is the earlier work, and not the later refined work, maybe you should update your studies. (Note this creates Z, not N)
Note, as I understand it, that initial Zermelo Set Theory didn't even HAVE "induction", but its last axiom was the Axiom of Infinity that say that there exists in this domain the set Z that contains the null set as an element and is so constituted that to each of its element a, there corresponds a further element of the form {a}, in other words with each of its elements a, it also contains the corresponding set {a} as an element.
Note, this is NOT the statement of induction.