The Math Forum

Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Math Forum » Discussions » sci.math.* » sci.math

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: Anti-foundation axiom
Replies: 11   Last Post: Mar 15, 2013 6:00 AM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Shmuel (Seymour J.) Metz

Posts: 3,473
Registered: 12/4/04
Re: Anti-foundation axiom
Posted: Mar 12, 2013 10:40 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

In <>, on 03/12/2013
at 02:28 PM, "K_h" <> said:

>This is not a correct characterization of set theory. In the
>generally accepted approach, not everything is a set and no
>collection can be a member of itself. Collections are bifurcated
>into two types and they are sets and proper classes. So
>"Everything is a set" just isn't part of modern theory.

There is no "everything" in modern set theory. What you have described
applies to GBN but not to ZFC, where the universe of discourse
includes only sets.

>Controversy exists over whether or not there exists
>non-constructible sets,

Controversy exists over whether to allow axiom systems that permit
non-constructible sets, but there is no controversy over whether there
are non-constructible sets in, e.g., ZFC.

Shmuel (Seymour J.) Metz, SysProg and JOAT <>

Unsolicited bulk E-mail subject to legal action. I reserve the
right to publicly post or ridicule any abusive E-mail. Reply to
domain Patriot dot net user shmuel+news to contact me. Do not
reply to

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2018. All Rights Reserved.