[FOM] From Compactness to Completeness

[G. Aldo Antonelli]

On 12/24/10 12:25 PM, T.Forster at dpmms.cam.ac.uk wrote:

> I think if the language is countable you don'tneed KL, surely?

Well, it seems to me that prima facie you do (but perhaps there is a 
clever way around it?):

A non terminating tree is one that, for every n, contains a branch that 
does not close at level n. KL is needed to obtain an infinite branch 
(which in turn gives the counter-model).

This is true even for a countable language.

Am I missing something?

-- Aldo


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G. Aldo Antonelli
Professor of Philosophy
University of California, Davis
http://philosophy.ucdavis.edu/antonelli
antonelli at ucdavis.edu +1 530 554 1368