Re: arithmetic in ZF
On 1 May 2005 14:32:17 -0700, Ross A. Finlayson <raf@xxxxxxxxxxxxxxx> said:
> I think ZF is inconsistent, because of regularity,
Well, you should stop thinking that, because if ZF is inconsistent, so
is ZF without regularity.
> In ZF there is the Burali-Forti paradox,
No there isn't (assuming ZF isn't inconsistent for other reasons). The
axioms do not permit the construction of the BF paradox.
.
Relevant Pages
- Re: arithmetic in ZF
... >>> I think ZF is inconsistent, because of regularity, ... >> Well, you should stop thinking that, because if ZF is inconsistent, so ... > But, I think quantification implies a universal set, ... assert flat out that quantification implies a universal set; ...
(sci.logic) - Re: Cantor and the binary tree
... > Ross A. Finlayson wrote: ... > derive a contradiction or reference an article where one is proved. ... Where the set of all set is itself a set, and regularity says it's not, ... ZF is inconsistent, because those axioms purport to describe all sets, ...
(sci.math) - Re: arithmetic in ZF
... >> I think ZF is inconsistent, because of regularity, ... > Well, you should stop thinking that, because if ZF is inconsistent, ... the set of all ordinals would appear to be the same form ... functions between physical objects are themselves physical objects. ...
(sci.logic) - Re: Is this theory consistent
... inconsistent, because it is too simple to be true, ... for all m exist!y P, it is obvious replacement would result at ... favorably one can add axiom of Regularity. ... Without Regularity the following formula in replacement can be proved. ...
(sci.logic) - Re: Ramification Schema.
... Without Regularity ... it becomes inconsistent. ... A consistent theory is not made inconsistent by deleting an ... axiom. ...
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