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

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Aatu Koskensilta

Posts: 2,638
Registered: 6/28/08
Re: Ordinals describable by a finite string of symbols
Posted: Jul 10, 2013 7:40 AM
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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 Logico-Philosophicus



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