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Topic: Ordinals describable by a finite string of symbols
Replies: 27   Last Post: Jul 8, 2013 9:56 PM

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 fom Posts: 1,968 Registered: 12/4/12
Re: Ordinals describable by a finite string of symbols
Posted: Jul 5, 2013 9:42 PM

On 7/4/2013 11:42 PM, apoorv wrote:
>
> Unless the ' the set of all nameable ordinals' is itself not a sharply
> Defined entity.

A short time ago, I began a thread with these

http://mathoverflow.net/questions/44102/is-the-analysis-as-taught-in-universities-in-fact-the-analysis-of-definable-numb/44129#44129

http://de.arxiv.org/pdf/1105.4597v2

In the second link you will find the remark:

"In a model of set theory, this property
strengthens V=HOD, but is not first-order
expressible"

You may take that as confirmation that "nameable ordinals"
(in so far as the modern paradigm would associate that
with the notions of definability used in the paper)
are not "sharply defined".

The notion of "sharply defined" would correspond with
the idea of "definite totalities" that I discussed with
you in an earlier post.

Or, comply more closely with the statement itself, note
that first-order logic involves certain presuppositions
regarding denotation (as noted elsewhere, denotation
without instantiation is a notion that may be compared
with Russellian description theory). This is stated
explicitly in the first sentence of the link:

http://plato.stanford.edu/entries/logic-free/

What is involved here, however, is that the instantiation
of a denotation in set theory will presuppose a "definite

In general, mathematicians might not be committed to
first-order logic. But, it is important to most in the
study of set theory.

it is really only applicable in a first-order context.

elsewhere.

Date Subject Author
7/5/13 fom
7/5/13 fom
7/6/13 Shmuel (Seymour J.) Metz
7/7/13 Peter Percival
7/7/13 fom
7/8/13 Shmuel (Seymour J.) Metz
7/8/13 fom
7/5/13 fom
7/5/13 fom
7/6/13 LudovicoVan
7/6/13 fom
7/6/13 LudovicoVan
7/6/13 fom
7/6/13 LudovicoVan
7/7/13 LudovicoVan
7/7/13 LudovicoVan
7/7/13 fom
7/7/13 LudovicoVan
7/7/13 fom
7/7/13 LudovicoVan
7/7/13 fom
7/7/13 LudovicoVan
7/7/13 fom
7/8/13 apoorv
7/7/13 fom
7/7/13 LudovicoVan
7/7/13 fom