Re: The set of necessary FISONs

On 2/28/2025 12:04 PM, WM wrote:

On 28.02.2025 16:52, Jim Burns wrote:

An inductive proof only proves about
a set which is its.owcn.only.inductive.subset,
like Z₀ and like ℕ, perhaps not like Z

>
Z contains many inductive subsets.

(We don't know whether Z=Z₀ or Z≠Z₀)
Consider this WM.inductive.proof:
⎛ Assume you prove {i:Aᶻ(i)} ⊆ Z is inductive.
⎜ Aᶻ is a predicate on Z
⎜
⎜ Which (inductive) subset of Z is {i:Aᶻ(i)} ?
⎜
⎜ Assume k ∈ Z
⎜ Which is true, Aᶻ(k) or ¬Aᶻ(k), and
⎝ how do you justify your answer?