I think I am a bit confused and likely just miss a key definition somewhere, so I'll just ask a naive question:
From N in V you have constructed 'N in *V. You argue that 'N contains N (in a specific sense) but also non-standard numbers (represented by non-constant sequences such as [(0,1,2,3,...)]). Then you observe that 'N is the initial model of PA in *V from which you conclude that ('N,*V) is not the example we want.
But as I understand it, you just showed that 'N is richer than N, in particular it contains non-standard elements. And to reduce to only elements of the type [(a,a,a,...)] which correspond to N wihtin 'N would correspond to a non-initial model, right?
So why isn't this the example you want?
papalex
npub1w8…9a0pl
2026-05-07 09:33:17 UTC
in reply to nevent1q…lfzn
Author Public Key
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wss://relay.momostr.pinkPublished at
2026-05-07 09:33:17 UTCEvent JSON
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"content": "I think I am a bit confused and likely just miss a key definition somewhere, so I'll just ask a naive question:\n\nFrom N in V you have constructed 'N in *V. You argue that 'N contains N (in a specific sense) but also non-standard numbers (represented by non-constant sequences such as [(0,1,2,3,...)]). Then you observe that 'N is the initial model of PA in *V from which you conclude that ('N,*V) is not the example we want.\n\nBut as I understand it, you just showed that 'N is richer than N, in particular it contains non-standard elements. And to reduce to only elements of the type [(a,a,a,...)] which correspond to N wihtin 'N would correspond to a non-initial model, right? \n\nSo why isn't this the example you want?",
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