Re: FOL & completeness


"Frederick Williams" <Frederick.Williams1@xxxxxxxxxxxxxxxxxxxxxxxxx> ha
scritto nel messaggio news:44BA34F8.1D33C8A6@xxxxxxxxxxxxxxxxxxxxxxxxxxxx
bargiax wrote:

I am very very confused about the completeness of FOL and the Goedel
result
of indecidibility.
Completeness: S|=F iff S|-F (or Val = Prov).

Goedel theorem for PA (that is a FO theory) says that there is a sentence
wich cannot be proven or disproven. I think that such a formula (or its
negation) should be in Val, right...? But if it is in Val then (for the
completeness statement) there must be a proof of it... help me to
understand, please!

PA may be a FO theory but it isn't first order logic. PA has a
successor function and some axioms governing it, so more things are
provable.


Can you show me which precisely are the axioms of PA that aren't FO?


.

Relevant Pages

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  • FOL & completeness
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    (sci.logic)