[FOM] Closure ordinal for Kripke construction?

[Stanislav Speranski]

Dear Chris,

>(1) Is there a published proof of this?

I don't know where such a proof was first published. However, here is the
proof which I tend to prefer:

_______ (2017) Notes on the computational aspects of Kripke’s theory of
truth. Studia Logica 105(2), 407–429.
http://doi.org/10.1007/s11225-016-9694-8

The advantage is that the corresponding argument is both relatively simple,
involving only the basic machinery of constructive ordinals, and rather
general, applying to various valuation schemes (these include the strong
Kleene scheme, of course) and leading to a somewhat deeper understanding of
an interesting source of intensionality related to the weak Kleene scheme
(for which the closure ordinal depends on the choice of Goedel numbering,
as was shown by Cain and Damnjanovich in their paper from 1991). Hope this
helps.

Best regards,
Stanislav
-----
http://math-cs.spbu.ru/~speranski/


On 21 November 2017 at 17:05, Chris Scambler <cscambler at gmail.com> wrote:

> In the paper "Outline for a Theory of Truth", Kripke states without proof
> that the Church-Kleene ordinal is the closure ordinal for his fixed point
> construction over the standard model of arithmetic.
>
> (1) Is there a published proof of this?
> (2) Is the result known to transfer to arbitrary structures M (as in, the
> closure ordinal for the Kripke construction over M is the least admissible
> over M)?
>
> cheers
>
> C
>
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