Post #2264417
2026-05-06 14:35 UTC
@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/
Replies (1)
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@typeswitch@gamedev.lgbt 2026-05-06 14:37
@johncarlosbaez@mathstodon.xyz @papalex@mathstodon.xyz This W contains *V by mapping each [(X₀ , X₁ , X₂ , ...)] to (the class of) the set of sequences [ X₀ × X₁ × X₂ × ... ] (up to a U-large set of indices). So that standard N maps to the [ N × N × N × ... ] and therefore contains both standard natural numbers (0,0,0,...), (1,1,1,...), (2,2,2,...), ... and nonstandard natural numbers (0,1,2,...), (1,2,3,...), (0,0,1,1,2,2,...). 7/