FOM: CH

[Kanovei]

<Date: Tue, 17 Mar 1998 04:28:32 -0500
<From: Robert Tragesser <RTragesser at compuserve.com>

< ... that he (Feferman) is not
<clear about the significance of the proof of the =
<independence of CH. 
....
<What surely is at issue is what its 
[independence of CH] 
<import is.  What,
<for example, does it say about the definiteness or
<determinateness of the continuum problem as a mathematical
<problem?  What is its import for mathematics? 

Questions around CH are interesting and important for 
those who

1) agree that both R and omega_1 are legitimate 
   mathematical objects,

2) agree that they are of key foundational importance 
   because they symbolize two principal ways as how one 
   gets uncountable sets from countable, 

3) conclude that the question of the relative size of R 
   and omega_1 is of key foundational importance as well. 

On the other hand, this circle of ideas "imports" little 
if any for finitarians, provists, perhaps categorists 
just because R, omega_1, and their interrelations are 
different in different "topoi" (and meaningless in the 
most of them). 

Vladimir Kanovei