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 <mailto: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

Brent

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