fom
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Registered:
12/4/12


Re: Matheology S 224
Posted:
Apr 20, 2013 10:59 AM


On 4/20/2013 5:25 AM, Alan Smaill wrote: > Frederick Williams <freddywilliams@btinternet.com> writes: > >> Nam Nguyen wrote: >>> >>> On 19/04/2013 5:55 AM, Frederick Williams wrote: >>>> Nam Nguyen wrote: >>>>> >>>>> On 18/04/2013 7:19 AM, Frederick Williams wrote: >> >>> >>>> >>>>>> Also, as I remarked elsewhere, "x e S' /\ Ay[ y e S' > y e S]" doesn't >>>>>> express "x is in a nonempty subset of S". >>>>> >>>>> Why? >>>> >>>> It says that x is in S' and S' is a subset of S. >>> >>> How does that contradict that it would express "x is in a nonempty >>> subset of S", in this context where we'd borrow the expressibility >>> of L(ZF) as much as we could, as I had alluded before? >> >> You really are plumbing the depths. To express that x is nonempty you >> have to say that something is in x, not that x is in something. > > but the claim was that x *is in* a nonempty set  > in this case S', which is nonempty, since x is an element of S', > and S' is a subset of S. > > (Much though it would be good for Nam to realise that > some background set theory axioms would be kind of useful here) >
Yes. I thought about posting some links indicating that primitive symbols are undefined outside of a system of axioms (definitioninuse)
The other aspect, though, is that Nam appears to be using an implicit existence assumption. So,
AxASES'(xeS' /\ Ay(yeS' > yeS))
clarifies the statement and exhibits its secondorder nature. This is fine since he claims that his work is not in the object language.

