From: Andrej Bauer <andrej.bauer@andrej.com>
To: James Lipton <jlipton@wesleyan.edu>
Cc: Categories <categories@mta.ca>
Subject: Re: size_question
Date: Sat, 2 Jul 2011 14:24:03 +0200 [thread overview]
Message-ID: <E1Qd4sZ-0005Ry-Sj@mlist.mta.ca> (raw)
In-Reply-To: <E1Qbuhe-0002c4-OV@mlist.mta.ca>
On Wed, Jun 29, 2011 at 4:43 AM, James Lipton <jlipton@wesleyan.edu> wrote:
> These are the "hereditarily finite sets"
>
> V(0) = empty set
>
> V(n+1) = P(V(n))
>
> V(omega) = U{V(n): n in omega}
>
> I would not call it "the" cat of finite sets, since there uncountably many
> countable models of ZF. Obviously the choice of ZF, rather than say Zermelo
> set theory or some other foundation is also pretty arbitrary.
I should think that the hereditarily finite sets do not depend all
that much on the background setting. After all, there are not very
many of them and they are quite concrete. Can they really be hugely
different depending on whether we work in ZF, ZFC, IZF, CZF etc?
With kind regards,
Andrej
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
next prev parent reply other threads:[~2011-07-02 12:24 UTC|newest]
Thread overview: 6+ messages / expand[flat|nested] mbox.gz Atom feed top
2011-06-28 17:39 size_question Eduardo Dubuc
2011-06-29 2:43 ` size_question James Lipton
2011-07-02 12:24 ` Andrej Bauer [this message]
2011-07-02 20:05 ` size_question Thomas Streicher
2011-07-03 15:01 ` size_question F. William Lawvere
2011-06-29 7:01 ` size_question Gaucher Philippe
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