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Matheology § 220
Posted:
Feb 13, 2013 9:29 AM


Matheology § 220
PA {{PeanoArithmetik}} already tells us that the universe is infinite, but PA ?stops? after we have all the natural numbers. {{No, Peano arithmetics never stops because it never reaches an end. Here potential and actual infinity are confused.}} ZFC goes beyond the natural numbers; in ZFC we can distinguish different infinite cardinalities such as ?countable? and ?uncountable?, and we can show that there are infinitely many cardinalities, uncountably many, etc. {{and we can show that there is nothing of that kind other than in dreams, but not in logic.}} [Saharon Shelah: "Logical Dreams" (2002)] http://arxiv.org/PS_cache/math/pdf/0211/0211398v1.pdf
Regards, WM



