2026-08-29T11:56:57Z https://yabu.me Evan Washington https://yabu.me/npub1thqhwm79yq74s0w4dc4et4j6pmnejwq23trt3jcff5tvz6c0n09saz5378 https://media.mathstodon.xyz/accounts/avatars/109/304/229/196/083/281/original/ae2110ad225b5b1f.png https://media.mathstodon.xyz/accounts/avatars/109/304/229/196/083/281/original/ae2110ad225b5b1f.png https://yabu.me/nevent1qqszlx50rjmwvqrr0ktesz5lx7z0yh465sk75l5ywldn8gkcamghavszypwuzam0c5sr6kpa64hzh9wktg8w0xfcp29vdwxtp9x3dsttp7dukcvxrsp In reply to <a href='/nevent1qqsyctxl3u4xapz9lrpemqvj6kmu7q67nlzwmj5e6zw5xkd4dlm47qqfs3ea2'>nevent1q…3ea2</a><br/>_________________________<br/><br/>This framing seems rather bizarre to me. I&#39;ll try to explain why:<br/><br/>Okay, so the theory of groups isn&#39;t categorical. And neither is set theory.<br/><br/>But (1) you don&#39;t need Gödel&#39;s incompleteness theorem to see this? And (2) we know of theories which *are* categorical, so it&#39;s not entirely naive to imagine that we might manage to cook another up.<br/><br/>(3) Even if you shouldn&#39;t be surprised in the case of sets (and I&#39;m not so sure about that), I think you *should* be surprised in the case of arithmetic. <br/><br/>We know exactly what the intended model is. We might hope that it&#39;s more like writing down axioms for one particular group rather than for all groups.<br/><br/>But consider the complete theory of true arithmetic (i.e. Th(N) in the language of Peano arithmetic). Gödel&#39;s theorem does tell us something about this theory (that we cannot effectively axiomatize it) but nothing (directly) about its categoricity. And of course, there are *many* other countable models of Th(N), basically as many as possible. 2026-04-26T01:34:22Z https://yabu.me/nevent1qqsxqs90m2x6ww0u3zv4x9qarlk5a50qdctjt6p67xs93838ndnk7cgzypwuzam0c5sr6kpa64hzh9wktg8w0xfcp29vdwxtp9x3dsttp7duk4y002a In reply to <a href='/nevent1qqsgjqwnl5yvu8j4lc6xeem5kv73qzvg74qqrm2r09z4zrlxvj5hccgl2ntja'>nevent1q…ntja</a><br/>_________________________<br/><br/>yeah! that&#39;s better! 2024-09-13T19:35:46Z https://yabu.me/nevent1qqs0ezc27sctyvmxfsr0djhmjyy2eqxmwdwvsdmtdjysus4ak4k0rdszypwuzam0c5sr6kpa64hzh9wktg8w0xfcp29vdwxtp9x3dsttp7duk2euhdv here to start a fight: to be a number is to be an element of a ring 2024-09-12T21:14:59Z