FOM: Re: Hersh on the axiom of infinity etc.
podnieks at cclu.lv
Fri Sep 18 01:57:48 EDT 1998
Hersh 12 Sep 1998 18:06:45 writes:
> One famous difficulty is [the] axiom of infinity. You can't
> 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).
University of Latvia, Institute of Mathematics and Computer
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