[FOM] indepence and consistency results of set theory

[Jesse Alama]

Figure 1 of Chapter 1 of Krivine's book does contain a figure showing  
a directed graph in which the axiom of extensionality fails.   
Probably every other axiom fails in that graph, too, so it doesn't  
show that extensionality is independent of any other axioms.  There  
are no other figures in the book.

Jesse

On Apr 30, 2005, at 7:14 AM, Matt Insall wrote:

> F. A. Muller asked about literature that deals with independence  
> results for
> the axioms of set theory (other than the ``famous'' ones like AC  
> and CH).
> When I was a graduate student, I read through a little book (100  
> pages) by
> J.L. Krivine, called ``Theorie axiomatique des  
> ensembles'' (``Introduction
> to axiomatic set theory'') (Translated into English by David  
> Miller).  As I
> recall (but I am a bit rusty on this), for some of the axioms, Krivine
> presents models that can be drawn on the page (i.e. for these  
> fragments of
> set theory, there are models with a very small finite number of  
> sets).  It
> seems to me that I could ``see'' the independence of certain of the  
> axioms
> from others by looking at the figures and reading his discussion of  
> them,
> even though Krivine may not have explicitly written much about the
> independences.  I never took the time to write out formal proofs of  
> the
> independence relations however.
>
> Matt
>
>> From a sunny day after the rain in the Missouri Ozarks.
>>
>
> Dr. Matt Insall
> Associate Professor of Mathematics
> Department of Mathematics and Statistics
> University of Missouri - Rolla
> Rolla MO 65409-0020
>
> insall at umr.edu
> (573)341-4901
>
>
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