On Fri, 21 Mar 2014 09:13:41 +0000
Andrew Butterfield <andrew.butterfi...@scss.tcd.ie> wrote:
> Is this the document kanananaskis-9-logic.pdf?
>
> If it is, I have a query: in Sec 1.1 Introduction (p9) we are shown
> some properties
>
> One is *Inhab* : U does not contain empty sets - fair enough
> Another is *Pow* which says that if X is in U, then so is P(X) =
> { Y : Y subseteq X } To me this implies that P(X) may (will) contain
> the empty set as an element.
>
> Is this a correct interpretation of the consequences of these rules?
First of all, this is rather unrelated to the topic of this thread,
so I am starting a new thread as I think you should have done.
To answer your actual question, the fact that PX is in U and the empty
set is in PX does not imply that the empty set is in U. In the usual
language of ZF/ZFC, U is not assumed to be transitive. Indeed, the next
page shows an explicit construction of U in ZFC.
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