Re: Definition of finite.

On May 3, 7:38 pm, hru...@xxxxxxxxxxxxxxxxxxxx (Herman Rubin) wrote:

All versions of set theory of which I am aware have an
axiom which guarantees an infinite set.
..................
Zuhair wrote:

Not all set theories has such an axiom, take for example
Kripke-Platek set theory with urelements.
Now it would be interesting to see how one can define
natural number in Z-I-R

I propose the following definition of x is a natural number in Z-I-R

x is a natural number <-> x is ordinal.

I think this would do the job.

However in this theory there is no need to define x is finite, since
every x in Z-I-R is finite.

Zuhair


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