Re: incompleteness of first-order logic

Li Yi wrote: 
T is Complete, if for any sentence p, it holds T |/- p => T |- not p.

How to prove it in propositional logic? 
In propositional logic, you have Th M |= A
iff A element of Th M.

Could you please show a concrete example to
Th M |/= forall y R(c,y)
Th M |/= exists y not R(c,y).
The book written by my teacher says it is true in first-order logic.

Maybe a badly written book, or
I was too quick.

I think M must be at least countably
infinite, otherwise Th M is again
complete.

Example comming soon.

Bye


.

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