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From: c...@tiac.net (Richard Harter)
Newsgroups: sci.logic,sci.math,comp.theory,sci.physics,alt.psychology.personality
Subject: Re: A Guide for Cantor Cranks
Date: Sat, 12 Mar 2011 18:56:50 GMT
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On 12 Mar 2011 21:23:35 +0200, Aatu Koskensilta
<aatu.koskensi...@uta.fi> wrote:

>c...@tiac.net (Richard Harter) writes:
>
>> That's the essence of the matter.  Godel's L is a minimal universe
>> satisfying ZF.  L isn't the only countable model for ZF; there are
>> many.
>
>  As usually understood L, Gödel's constructible universe, is not
>countable -- it is a proper class. L is minimal in the sense that it
>is contained in any inner model of set theory. (There is also a
>countable ordinal alpha such that L_alpha is the minimal standard
>model of ZF.)

Right.  Thanks for being precise.

>
>> The trouble with the "entire conceptual power set" is that you can't
>> guarantee it with any finite set of axioms.
>
>  What sort of guarantees do you have in mind?