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Date: Jul 21, 2008 21:03
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Author: raul.ianraul.ian
Date: Jul 21, 2008 20:55
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Author: revanthrevanth
Date: Jul 21, 2008 20:06
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Author: ZaljoharZaljohar
Date: Jul 21, 2008 19:52
Hi all,
What prevents the existence of a set of all sets in ZFC, is actually
separation. It appears to me that the other axioms that do not entail
separation nor regularity nor choice, will not be contradictive with
the existence of the set of all sets. Two axioms that of intersection
and that of complementary class, do not exist in ZFC, which is in my
opinion a point of weakness, since these axioms seems pritty
intuitive.
In the following theory, all axioms of Z except separation and
regularity are presented in unrestricted manner. In addition all
axioms of ZFC are presented relativized to V ( the class of all
sets ), in addition you have axiom of intersection and axiom of
complementary sets in unrestricted manner. This of course will lead to
the existence of the class of all classes.
Theory /\ is the set of all sentences entailed by (using FOL with
identity and the primitives "in" and "V" were V is a constant) the
following non logical axioms:
Definition: x is a set iff x in V
Definition: x is a class iff [ x in V or ~ x in V ]
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Author: RupertRupert
Date: Jul 21, 2008 18:27
I was wondering if anyone could possibly let me know where to find a
proof that if ZF is consistent, then ZF+DC is strictly stronger than ZF
+ACC. (Here by ACC I mean the axiom of countable choice).
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