Re: FOL and AST

On Jun 12, 12:15 am, Marc Alcobé García <malc...@xxxxxxxxx> wrote:
On 12 jun, 07:53, herbzet <herb...@xxxxxxxxx> wrote:

As for uncountable languages, I don't see why we should be much
interested in such highly theoretical objects.

As a possible answer, Shoenfield defines validity in a structure by
adding to the language a constant for each individual.
I do not know if it is possible to avoid this expansion of the
language in that definition. But if it was not, then the need for
uncountable languages would not be of any high theoricity, but a quite
basic need.

We don't have to use that method. We can define satisfaction and truth
in a structure (what Shoenfield calls 'validity', as opposed to the
more ordinary sense of 'validity' as 'satisfied or true in all
structures') with an uncountable universe without having to use a
method of adding constants.

That there are other uses for uncountable languages though is another
matter.

MoeBlee


.

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