typeswitch on Nostr: I.e. [(X₀ , X₁ , X₂ ...)] = [(Y₀ , Y₁ , Y₂ ...)] iff { i : Xᵢ = Yᵢ } ...

I.e.

[(X₀ , X₁ , X₂ ...)] = [(Y₀ , Y₁ , Y₂ ...)] iff
{ i : Xᵢ = Yᵢ } ∈ U

and

[(X₀ , X₁ , X₂ ...)] ∈ [(Y₀ , Y₁ , Y₂ ...)] iff
{ i : Xᵢ = Yᵢ } ∈ U

This gives a nonstandard model of ZFC that contains V by mapping each set onto the equivalence class that contains the sequence where that set is every element:

X in V ↦ [(X, X, X, ...)] in *V

Let's call this class 'X.

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