[FOM] Dual of Dedekind-infiniteness.
lstout at iwu.edu
Sun Oct 7 19:15:26 EDT 2007
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
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?
Professof of Mathematics
Illinois Wesleyan University
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