[FOM] Dual of Dedekind-infiniteness.

[Lawrence Stout]

I looked at the variants on Dedekind finiteness in two papers:
"Dedekind Finiteness in Topoi", JPAA 49 (1987), 219-225
"Finiteness Notions in Fuzzy Sets", Fuzzy Sets and Systems, Vol.124  
No. ER1 (2001?)

Neither of these is directly answering your question since they lie  
outside the narrower setting of ZF or ZFC.  I remember that both  
Sierpinski and Tarski had a lot to say about these.  Jech's book on  
the axiom of choice gives some of the variants.  Troelstra  also has  
a paper giving a large number of different intuitionistic variants on  
finite.

In general, nailing down what "finite" means can be very difficult.


On Oct 5, 2007, at 11:16 PM, Bill Taylor wrote:

> Does anyone know if the following "dual" of Dedekind-infinitude
> has been studied?



Lawrence Stout
Professof of Mathematics
Illinois Wesleyan University