[FOM] From Compactness to Completeness

[T.Forster@dpmms.cam.ac.uk]

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?
>
>