Post #2264400
2026-05-06 01:54 UTC
losing my mind over the highlighted sentence. in other words. in a nonstandard model of peano arithmetic, you can have "infinite" natural numbers. in some nonstandard model of set theory, the standard model of peano arithmetic has infinite natural numbers, and you need a nonstandard model of peano arithmetic to exclude them.
Replies (3)
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@typeswitch@gamedev.lgbt 2026-05-06 01:55
first-order logic is hilariously full of holes like this.
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@hllizi@hespere.de 2026-05-06 07:03
@typeswitch@gamedev.lgbt the accepted solution to this problem is not to think about it.
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@johncarlosbaez@mathstodon.xyz 2026-05-06 09:00
@typeswitch@gamedev.lgbt - I'm not sure that claim is true. I'd have to see a proof to believe it. It's a fairly subtle subject. If it's true, that's quite exciting to me, since I've spent some time trying to understand nonstandard models of PA in this conversation with Michael Weiss: https://diagonalargument.com/mathnotes/nonstandard-models-of-arithmetic-the-series/