On 16 Jan 2014, at 19:18, meekerdb wrote:

On 1/16/2014 12:38 AM, Bruno Marchal wrote:

On 15 Jan 2014, at 20:44, meekerdb wrote:

On 1/15/2014 12:29 AM, Bruno Marchal wrote:

On 14 Jan 2014, at 22:39, LizR wrote:

On 15 January 2014 10:29, Terren Suydam <terren.suy...@gmail.com> wrote:
condescending dismissal in 3... 2... 1...

Teehee.

Not a condescending dismissal in anyone else's mind, however, just more hand-waving nonsense that only Edgar could possibly think is a dismissal.

This is fun, in a masochistic sort of way, but I am starting to miss discussions with some real meat in them.

Ahaaaa ... Me too :)

Ready for a bit of (modal) logic? That is needed for the Solovay theorem, exploited heavily in the AUDA ...

I'd like to know what the existence of non-standard models of arithmetic, especially the finitist ones, implies for comp?

All non-standard models are infinite. They does not play any direct roles, except for allowing the consistency of inconsistency. A model which satisfies Bf has to be non standard. A proof of "false" needs to be an infinite "natural numbers", and it has an infinity of predecessors (due to the axiom saying that 0 is unique in having no predecessors).

I think that only refers to non-standard models which add not-G as an axiom where G is the Godel sentence. What about application of the compactness theorem to produce a non-standard model?

http://en.wikipedia.org/wiki/Non-standard_model_of_arithmetic

I was just using one special non standard model, to illustrate the use of a non standrad natural number (and ewplain that it has nothing to so with usual integer). But all non standard models have such infinite element, of course they are not in general capable of being interpreted into a "proof of false".

Bruno






Brent

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http://iridia.ulb.ac.be/~marchal/



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