23/04/03 15:52:37.17 tfbTcgqZ.net
>>41 追加引用
>構成的集合論(英語版)
下記に、Constructive set theory 構成的集合論(英語版)での 選択公理 Axiom of Choice に関する記述があります
なお、個人的には、>>35の Sergiu Hart氏のgame2が(フルパワーの)選択公理を使わない版なので
”選択公理と今回の時枝記事のトリックとの関連は薄いのでは”と考えています
(参考)
URLリンク(en.wikipedia.org)
Constructive set theory
Imposed restrictions on a set theory
Compared to the classical counterpart, one is generally less likely to prove the existence of relations that cannot be realized. Adopting the standard definition of set equality via extensionality, the full Axiom of Choice is such a non-constructive principle that implies PEM for the formulas permitted in one's adopted Separation schema, by Diaconescu's theorem. Similar results hold for the Axiom of Regularity in its standard form, as shown below.