[FOM] From theorems of infinity to axioms of infinity (Michael Detlefsen)
MartDowd at aol.com
MartDowd at aol.com
Tue Mar 12 13:38:20 EDT 2013
Dr. Ferreiros,
The existence of infinite sets is in fact a question which arises with
regard to the natural numbers. ZFC - infinity has the hereditarily finite
sets as a model. It does not have a finite model, analogously to PA, or even
Q (see
_http://mathoverflow.net/questions/51703/is-robinson-arithmetic-biinterpretable-with-some-theory-in-lst_
(http://mathoverflow.net/questions/51703/is-robinson-arithmetic-biinterpretable-with-some-theory-in-lst) ). The
universe of discourse of arithmetic is infinite and contains infinite
subsets, whose properties are readily studied using PA. An axiom must be added to
set theory, so that infinite sets are elemens of the universe of discourse.
- Martin Dowd
In a message dated 3/11/2013 3:16:11 P.M. Pacific Daylight Time,
josef at us.es writes:
One can actually show that the existence of infinite sets, and furthermore
the power set axiom, are intimately linked with the real numbers
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