Re: deductive databases
From: Jan Hidders <jan.hidders_at_REMOVETHIS.pandora.be>
Date: Mon, 23 May 2005 19:52:00 GMT
Message-ID: <Avqke.99355$Rk1.5615685_at_phobos.telenet-ops.be>
>
> You haven't specified that the structure contains + and *
> operations. Let's skip ahead a bit. Let L be the language of PA
> extended with two binary predicates p and q. By compactness, it is not
> the case that there is any set M of sentences in the language of L
> such that for every structure I obtained by adding to a model of PA
> two binary relations R and S interpreting p and q, I satisfies the
> sentences in M if and only if S is the transitive closure of R.
Date: Mon, 23 May 2005 19:52:00 GMT
Message-ID: <Avqke.99355$Rk1.5615685_at_phobos.telenet-ops.be>
Torkel Franzen wrote:
> Jan Hidders <jan.hidders_at_REMOVETHIS.pandora.be> writes:
>
>>Since we are doing PA they have to satisfy PA's axioms.
>
> You haven't specified that the structure contains + and *
> operations. Let's skip ahead a bit. Let L be the language of PA
> extended with two binary predicates p and q. By compactness, it is not
> the case that there is any set M of sentences in the language of L
> such that for every structure I obtained by adding to a model of PA
> two binary relations R and S interpreting p and q, I satisfies the
> sentences in M if and only if S is the transitive closure of R.
- Jan Hidders