Because you can't take arbitrary external subsets of sets in *V. Every infinite set in *V is going to have nonstandard elements. (You can create internal subsets following the rules of ZFC. E.g. consider a nonstandard natural n. The natural numbers less than n form a set by replacement (clamping N by n-1). But this isn't a (sub)model of PA, and it contains nonstandard numbers (e.g. n-1).)
That's why we construct W to let us build more interesting subsets.
azul
npub1e9…2vdd5
2026-05-07 12:19:18 UTC
in reply to nevent1q…gxy0
Author Public Key
npub1e9y64jhalql35k2cfhntmkvnnz5937pwrq0267578qrpty6uafzsc2vdd5Published at
2026-05-07 12:19:18 UTCEvent JSON
{
"id": "992e8c2fb6fc152674b4829b9cf33045e244c5fe84015130a665b492c91a4d32",
"pubkey": "c949aacafdf83f1a59584de6bdd99398a858f82e181ead7a9e380615935cea45",
"created_at": 1778156358,
"kind": 1,
"tags": [
[
"e",
"07e0b0015c937da8c8c83ee48a13501bdfe746c83b813c9b38d26dc0e96e01f9",
"",
"root",
"c949aacafdf83f1a59584de6bdd99398a858f82e181ead7a9e380615935cea45"
],
[
"e",
"c46354a6624b32876ef9371e9902cfc1eb662af2d2d741264e1c2148355ac6b2",
"",
"reply",
"71c8e85f2a58650389b64a78286c7c46d1de4bb91504af4d5ab1f3d8d7e0a36f"
],
[
"proxy",
"https://gamedev.lgbt/@typeswitch/116533255078695525",
"web"
],
[
"p",
"9a6a1a8eefd0b53d7e0c966ab35bd904151246f03b1be98fa0d2d0eeb4940320"
],
[
"p",
"71c8e85f2a58650389b64a78286c7c46d1de4bb91504af4d5ab1f3d8d7e0a36f"
],
[
"p",
"c949aacafdf83f1a59584de6bdd99398a858f82e181ead7a9e380615935cea45"
],
[
"proxy",
"https://gamedev.lgbt/users/typeswitch/statuses/116533255078695525",
"activitypub"
],
[
"L",
"pink.momostr"
],
[
"l",
"pink.momostr.activitypub:https://gamedev.lgbt/users/typeswitch/statuses/116533255078695525",
"pink.momostr"
],
[
"-"
]
],
"content": "Because you can't take arbitrary external subsets of sets in *V. Every infinite set in *V is going to have nonstandard elements. (You can create internal subsets following the rules of ZFC. E.g. consider a nonstandard natural n. The natural numbers less than n form a set by replacement (clamping N by n-1). But this isn't a (sub)model of PA, and it contains nonstandard numbers (e.g. n-1).)\n\nThat's why we construct W to let us build more interesting subsets.",
"sig": "fe39aaa4e10d0073862ea9b599b36a67b2b41641127c2adfee5d0f50971d6fbabf593b0cfc79eef52fa9db39068bdd8d6e4910a90261e723b59b2c41a2db0ed0"
}