Post #2264413
2026-05-06 14:30 UTC
@johncarlosbaez@mathstodon.xyz @papalex@mathstodon.xyz
So let's build a nonstandard model around V that has the property we want.
Let's start with an ultrapower of V with the naturals as index set, and call that *V. This is a nonstandard model of V parametrized by an ultrafilter U over the naturals N, where sets in *V are given by sequences (X₀ , X₁ , X₂ ...) of sets in V, quotiented by pointwise equality in a U-large set of indices, and the ∈ relation is given by pointwise membership in a U-large set of indices.
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Replies (1)
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@typeswitch@gamedev.lgbt 2026-05-06 14:31
@johncarlosbaez@mathstodon.xyz @papalex@mathstodon.xyz 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. 3/