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Topic: some amateurish opinions on CH
Replies: 57   Last Post: Apr 16, 2013 8:12 PM

 Messages: [ Previous | Next ]
 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 972-975, Vol. 39, 1653, Proc. N.A.S.
>
>

The paper seems to be at a for-profit 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.

Date Subject Author
4/7/13 fom
4/7/13 mueckenh@rz.fh-augsburg.de
4/7/13 Bergholt Stuttley Johnson
4/7/13 dan.ms.chaos@gmail.com
4/7/13 mueckenh@rz.fh-augsburg.de
4/7/13 dan.ms.chaos@gmail.com
4/7/13 mueckenh@rz.fh-augsburg.de
4/7/13 dan.ms.chaos@gmail.com
4/7/13 mueckenh@rz.fh-augsburg.de
4/7/13 Virgil
4/8/13 dan.ms.chaos@gmail.com
4/8/13 mueckenh@rz.fh-augsburg.de
4/8/13 dan.ms.chaos@gmail.com
4/8/13 mueckenh@rz.fh-augsburg.de
4/8/13 dan.ms.chaos@gmail.com
4/8/13 mueckenh@rz.fh-augsburg.de
4/8/13 Virgil
4/8/13 Virgil
4/9/13 apoorv
4/8/13 Virgil
4/7/13 Virgil
4/9/13 Guest
4/9/13 dan.ms.chaos@gmail.com
4/9/13 fom
4/10/13 Guest
4/10/13 dan.ms.chaos@gmail.com
4/10/13 fom
4/10/13 JT
4/11/13 apoorv
4/11/13 dan.ms.chaos@gmail.com
4/11/13 apoorv
4/11/13 fom
4/15/13 apoorv
4/15/13 fom
4/16/13 Shmuel (Seymour J.) Metz
4/16/13 fom
4/7/13 Virgil
4/7/13 William Elliot
4/7/13 fom
4/7/13 fom
4/8/13 William Elliot
4/8/13 fom
4/9/13 William Elliot
4/9/13 fom
4/9/13 William Elliot
4/9/13 fom
4/9/13 dan.ms.chaos@gmail.com
4/9/13 fom
4/9/13 dan.ms.chaos@gmail.com
4/9/13 fom
4/9/13 dan.ms.chaos@gmail.com
4/9/13 fom
4/10/13 fom
4/11/13 dan.ms.chaos@gmail.com
4/11/13 fom
4/11/13 dan.ms.chaos@gmail.com
4/11/13 fom
4/9/13 fom