Re: The set of necessary FISONs

On 3/1/2025 1:28 PM, WM wrote:

On 01.03.2025 18:47, Jim Burns wrote:

On 3/1/2025 7:51 AM, WM wrote:

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Z_0 contains only 0, {0}, {{0}}, ...

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Z₀ = {0,{0},{{0}},...} is
the only subset of Z₀ which
holds 0 and, for each a, holds {a}

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Z₀ is defined by induction.

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inductive(Z)
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inductive(Z) :⇔ 0∈Z ∧ ∀a:a∈Z⇒{a}∈Z
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Z₀ is the emptiest (<EZ>"einfachste"?)
inductive set.
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inductive(W) ⇒ Z₀ ⊆ W
inductive(Z₀)
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Z₀ is not constructed by supertask.
Z₀ = ⋂𝒫ⁱⁿᵈ(Z)
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Likewise UF is defined by induction.
ℕ \ F(1) \ F(2) \ F(3) \ ... = ℵo
= ℕ \ (F(1) U F(2) U F(3) U ...) = ℵo.
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In narrower Z₀,
inductivity identifies a unique set.

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So it is.

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Thank you.
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{S⊆Z₀:inductive.S} = {Z₀} ∧
inductive{i:A(i)}  ⇒
{i:A(i)} ∈ {SsZ₀:inductive.S} = {Z₀}  ⇒
Z₀ = {i:A(i)}
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Z₀ = {i:A(i)} ∧
∀n ∈ {i:A(i)}: A(n)  ⇒
∀n ∈ Z₀: A(n)
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Our inductive conclusions are justifiedly universal
because they are in narrower Z₀
not because of any supertask.
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