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Topic:
Ordinals describable by a finite string of symbols
Replies:
3
Last Post:
Jul 11, 2013 8:42 PM




Re: Ordinals describable by a finite string of symbols
Posted:
Jul 10, 2013 7:40 AM


fom <fomJUNK@nyms.net> writes:
> What is expressed by both, however, is that the universe of discourse > must be expressed by a set  an object of the theory.
What is expressed by the axioms M and SM is that there exists a set with certain properties. Neither says anything whatever about the universe of discourse or how it must be expressed. In any case, for (relative) consistency and independence results by forcing, the use of M and SM is always eliminable, as Cohen himsels explains in _Set Theory and the Continuum Hypothesis_. (G. H. Moore, in /The Origins of Forcing/, reports Moschovakis in a letter urged Cohen to do away with the "ridiculous assumption", that there exists a standard model of set theory!)
 Aatu Koskensilta (aatu.koskensilta@uta.fi)
"Wovon man nicht sprechen kann, darüber muss man schweigen"  Ludwig Wittgenstein, Tractatus LogicoPhilosophicus



