fom
Posts:
1,968
Registered:
12/4/12


Re: some amateurish opinions on CH
Posted:
Apr 9, 2013 2:52 AM


On 4/9/2013 12:15 AM, William Elliot wrote: > On Mon, 8 Apr 2013, fom wrote: >> On 4/8/2013 11:24 PM, William Elliot wrote: >>> On Mon, 8 Apr 2013, fom wrote: >
<snip>
> >>>>> BTW, Quine's NF denies AxC. >>>> >>>> I need to look at Quine's work more carefully at this >>>> point. I doubt I would like it because I do not >>>> agree with his views on the nature of identity. >>> >>> At Quine's time it was assumed AxC was compatible. Decades later, it >>> turns out to be violated for some large constructed sets. Would you like >>> the reference for the paper? >> >> Yes. Thank you. > > Ernst P. Specker, "The Axiom of Choice in Quine's New Foundations > for Mathematical Logic," pp 972975, Vol. 39, 1653, Proc. N.A.S. > > I'd be interested in your comments. >
The paper seems to be at a forprofit journal.
I will do my best to do some quick reading on NF and material related to the citation.
But, just so you know, my axioms include
AxAy((Az(ycz > xez) /\ Ez(xez /\ ycz)) > Az((xez /\ ycz) > (Ew(xew /\ wcy) \/ Aw(zcw > ycw))))
which should have the same effect as Quine's stratified version of 'xey'
The antecedent is just taken from the definiens of the defining statement
AxAy(xey <> (Az(ycz > xez) /\ Ez(xez /\ ycz)))
And, as with Quine, part of my objective had been to introduce a universal class.

