[FOM] Re: Flexible Predicates

V.Yu.Shavrukov volodya at itu.dk
Fri Jun 11 03:58:49 EDT 2004

This is a comment on the recent discussion on the bibliometrical history
of flexible predicates.

The statement in Kripke's paper, as well as in Hájek & Pudlák is 
weaker than the one requested by Taranovsky:

> Is there an arithmetical formula phi with one free variable such that
> for every Pi-0-1 formula psi with one free variable it is consistent
> with Peano Arithmetic that
> Forall n (phi(n) <--> psi(n)).
> Can phi be a Pi-0-1 formula?

even though the proofs are sufficient to get Taranovsky's form.

The statement in the stronger Taranovsky's form occurs as Theorem 2.11 

P.Lindström. Aspects of Incompleteness 2nd ed. AKPeters 2003,

where it is also shown that there is a Delta_n formula that flexes
(in Taranovsky's sense) to all Beta_n formulas.

Volodya Shavrukov

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