Post #2264416
2026-05-06 14:33 UTC
@johncarlosbaez@mathstodon.xyz @papalex@mathstodon.xyz
So *V isn't the example we want. But we might imagine a nonstandard model that contains *V, but also allows us to take external subsets of the sets in *V, so that we could look at the standard natural numbers without the nonstandard natural numbers sneaking in.
5/
Replies (1)
-
@typeswitch@gamedev.lgbt 2026-05-06 14:35
@johncarlosbaez@mathstodon.xyz @papalex@mathstodon.xyz Here's the part I'm unsure about. I think we could build such a model by transposing the ultrapower construction, so instead of looking at ultrapowers of sets in V, we look at sets of sequences in V, quotiented by U, and build a model out of that. Let's call this model W, and the idea that sets in W are sets of sequences in V, up to equivalence on U-large sets of indices. And ∈ in W is given by ∈ in V, up to equivalence of sequences by U-large sets of indices. 6/