FOM: Re: Hersh on the axiom of infinity etc.

[Karlis Podnieks]

Hersh 12 Sep 1998 18:06:45 writes:

> One famous difficulty is [the] axiom of infinity.  You can't
do
> modern math without it.

There is a trivial (but usually ignored) fact about the axiom of
infinity mentioned by Skolem in 1950s (see Fraenkel and Bar
Hillel) - this axiom can be formulated as a  c o m p r e h e n s
i o n  a x i o m. Indeed, if you define:

x is natural number <-> x is a transitive set & x is well
ordered by the membership relation in  b o t h directions,

then you can put the axiom if infinity as follows:

EwAx(x in w <-> x is natural number).

Best wishes,
Karlis Podnieks
http://www.ltn.lv/~podnieks/
University of Latvia, Institute of Mathematics and Computer
Science