[FOM] Re. Is ConQ provable in Q?
Andrew Boucher
Helene.Boucher at wanadoo.fr
Sun Jun 5 12:49:46 EDT 2005
The example in that paper has V as a certain fixed point extension of S
v (x)(y)(x = y), where S is the conjunct of all the axioms of
Robinson's Q. As I may be misrecalling, Jeroslow also had the example
of {S v (x)(y)(x = y) : S is an axiom or instance of an axiom schema of
PA}. If that is so, does anyone have a reference? Did Jeroslow have
any more natural examples?
(From a cloudy Paris!)
On Jun 4, 2005, at 5:42 PM, mdetlef1 at nd.edu wrote:
>
> ...I think it worth mentioning a
> too-little known paper of the late Robert Jeroslow's. This is:
> "Consistency
> Statements in Formal Theories", Fundamenta Mathematicae 72 (1971):
> 17--40.
> Theorem 1.5 in that paper gives a (weak) theory V that is a subsystem
> of PA,
> that strongly represents all pr fncs and weakly represents all re sets
> and
> which proves a consistency sentence Con(V) constructed in the usual
> way from an
> axiomhood predicate that weakly represents the set of axioms of V and
> which has
> this form: (x)(Prov_V(x) ---> neq(x, [o=1 & not 0=1])), where neq(x,
> y) is the
> standard encoding of the pr relation 'not x=y'.
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