Re: Non-standard models of PA


"Torkel Franzen" <torkel@xxxxxxxxxx> ha scritto

>> I would like to see an explicit example of a non-standard model of PA
>> (first
>> order Peano Axioms), can anyone give me some reference?
>
> Take any standard Henkin-style proof of the completeness theorem for
> first order logic. It gives you a definable model of the theory
> obtained by adding to the language of PA a new constant c and to the
> axioms of PA the sentences (Ez)(c=s(z)), (Ez)(c=s(s(z))),...

Ok, it gives a non-standard model of PA but does it exist something easier
(like a (simple) definition of a set and operations) that does not require
sophisticated costruction like the Henkin's one?


.

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  • Re: Non-standard models of PA
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