20/05/10 10:23:13.23 mjl0bfS3.net
>>383
>However, the class existence axioms of NBG are restricted so that they only quantify over sets, rather than over all classes.
>This causes NBG to be a conservative extension of ZF.
つづき
ここ、実は ”conservative extension”にリンクが張ってあって、下記に飛べます（＾＾
URLﾘﾝｸ(en.wikipedia.org)
Conservative extension
(抜粋)
In mathematical logic, a conservative extension is a supertheory of a theory which is often convenient for proving theorems, but proves no new theorems about the language of the original theory.
Similarly, a non-conservative extension is a supertheory which is not conservative, and can prove more theorems than the original.
Contents
1 Examples
2 Model-theoretic conservative extension
(引用終り)
要は（＾＾
conservative extension：often convenient for proving theorems, but proves no new theorems about the language of the original theory
non-conservative extension：can prove more theorems than the original
ってこと
ZFCに対し、NBGは conservativeで、ZFCGは non-conservative です
（参考：本スレより転載）
Inter-universal geometry と ABC予想 52
ｽﾚﾘﾝｸ(math板:606番)
(抜粋)
606 名前：１３２人目の素数さん[] 投稿日：2020/05/09(土) 17:57:38.91 ID:/BYRDNlz
＞案の定ZFCGがZFCの保存的拡大だのZFCの9個の公理だの間違えまくってる
と書いてガゼで主張しただけだよ。
IUT-4で以下を修正しており、指摘で修正が必要であったのは、この箇所だよ。
concerning the “conservative extensionality” of ZFCG relative to ZFC, i.e.,
roughly speaking, that“any proposition that may be formulated in a ZFC-model and,
moreover, holds in a ZFCG-model infact holds in the original ZFC-model”
(引用終り)