typeswitch on Nostr: So let's build a nonstandard model around V that has the property we want. Let's ...

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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