From: weemba@sagi.wistar.upenn.edu (Matthew P Wiener)
Newsgroups: sci.logic,sci.math
Subject: Re: Prime Ideal Theorem in ZF
Date: 12 Jun 1998 13:18:06 GMT
In-reply-to: Paul WONG
In article <35808FE8.6A41@arp.anu.edu.au>, Paul WONG Is there any reference where I can find a list of
>equivalences, in ZF, of the Prime Ideal Theorem of Boolean Algebra?
Rubin and Rubin EQUIVALENTS OF THE AXIOM OF CHOICE
Schechter HANDBOOK OF ANALYSIS AND ITS FOUNDATIONS
Regarding the latter, see http://math.vanderbilt.edu/~schectex/ccc for
two gifs listing 27 PIT equivalents.
--
-Matthew P Wiener (weemba@sagi.wistar.upenn.edu)
==============================================================================
From: "Arthur L. Rubin" <216-5888@mcimail.com>
Newsgroups: sci.math
Subject: Re: INFINITE; definitions.
Date: Fri, 11 Dec 1998 11:07:24 +0700
Brian M. Scott wrote:
> Do you know whether anyone's yet settled the question of whether
> 'every linearly orderable topological space is normal' (LN) is
> equivalent to full AC? I remember that van Douwen showed quite a
> while ago that LN implies a weak form of countable AC.
According to Consequences of AC, available (in part) on the web
through my mother's web page at http://www.math.purdue.edu/~jer,
LN does not imply full AC. It is form 118 in that book, and holds
in the standard Cohen model denoted M1 in that book.
--
Arthur L. Rubin 216-5888@mcimail.com