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Topic: Few questions on forcing, large cardinals
Replies: 17   Last Post: Mar 30, 2013 1:21 PM

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fom

Posts: 1,968
Registered: 12/4/12
Re: Few questions on forcing, large cardinals
Posted: Mar 19, 2013 12:45 PM
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On 3/19/2013 10:17 AM, Ross A. Finlayson wrote:
>>
>> And yes, forcing is unobjectionable when you redefine truth.
>>
>> But, no one told anyone.

>
> If you might elucidate on that, it may help to establish the context a
> bit more firmly to the gallery.
>


It is not a mathematical issue.

Forcing changes what it means for something to
be true in mathematics if the outcome is to
define truth in terms of "truth persistence
under forcing".

Tarski-based semantics is replaced by the kind of
thing that is discussed in the book by Langholm.

To change the classical problem is not the same
as solving the classical problem.

For example, suppose it to be true that partial
systems are not diagonalizable.

I make this guess simply because a presumption
of the diagonal argument is a presumption that
"all" of the objects have been given a locus
in the list.

Non-diagonalizability is a "truth" of partial
systems.

It is not a truth of total systems.

So, what other "truths" are different?










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