19/10/12 11:56:57.56 0oc9Ztsl.net
>>287
申し訳ないが、意味が取れない
１）下記、Zermelo (1908b) ”(b) the existence, for any object a, of the singleton set {a} which has a as its sole member”
２）これは、>>175の通り、ZFCでは、対の公理で「a → {a}」が言える
３）で、Zermelo (1908b)では正則性公理は、無かった（∵1925年にジョン・フォン・ノイマンによって導入された）
４）しかし、ZFCの対の公理による「a → {a}」の the singleton set {a}生成 に、正則性公理からの規制（有限回に限られる？）があると、そういう話はないでしょ？
じゃ、ZFCの対の公理による「a → {a}」の the singleton set {a}生成が、これの超限回繰返しが可能なわけですよね
（>>224より）
URLﾘﾝｸ(plato.stanford.edu)
Stanford Encyclopedia of Philosophy
Zermelo’s Axiomatization of Set Theory Michael Hallett
First published Tue Jul 2, 2013
(抜粋)
1. The Axioms
Given this, the one fundamental relation is that of set membership, ‘ε’ , which allows one to state that an object a belongs to, or is in, a set b, written ‘a ε b’.[4] Zermelo then laid down seven axioms which give a partial description of what is to be found in B. These can be described as follows:
I.Extensionality
This says roughly that sets are determined by the elements they contain.
II.Axiom of Elementary Sets
This asserts
(a) the existence of a set which contains no members (denoted ‘0’ by Zermelo, now commonly denoted by ‘?’);
(b) the existence, for any object a, of the singleton set {a} which has a as its sole member; and
(c) the existence, for any two objects a, b, of the unordered pair {a, b}, which has just a, b as its members.
URLﾘﾝｸ(ja.wikipedia.org)
正則性公理（せいそくせいこうり、英: axiom of regularity）は、別名基礎の公理（きそのこうり、英: axiom of foundation） とも呼ばれ、ZF公理系を構成する公理の一つで、1925年にジョン・フォン・ノイマンによって導入された。