[FOM] From Compactness to Completeness

T.Forster@dpmms.cam.ac.uk T.Forster at dpmms.cam.ac.uk
Sat Dec 25 04:00:37 EST 2010

Maybe it is i who am missing something.. If the language is countableyou 
have a global ordering of the children at each node and this gives you a 
canonical way of picking the child you want? The vertices of the tree are 
decorated by fmlae of the language, no?

On Dec 25 2010, G. Aldo Antonelli wrote:

>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?

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