The "classical classical" is deliberate, as explained in the footnote.

On Sun, Feb 27, 2022 at 8:12 PM David A. Wheeler <[email protected]>
wrote:

>
>
> > On Feb 22, 2022, at 3:58 PM, Benoit <[email protected]> wrote:
> >
> >
> > Hi everyone,
> >
> > I uploaded yesterday a preprint to the arXiv titled "Independence
> questions in a finite axiom-schematization of first-order logic" (
> https://arxiv.org/abs/2202.10383).
>
> I just briefly skimmed it & it's really interesting! Thanks for writing it!
>
> I think we should modify some set.mm comments to specifically cite this
> work.
> At the least, modifying some of the axiom statements (like ax-11) to note
> that they've
> been proven (partially) independent & then citing this paper makes sense.
> Benoit: If you have suggestions, or even better pull requests, that'd be
> great.
>
> A nit: in the introduction we see "classical classical" in:
> > In this article, “first-order logic” means classical classical1
> one-sorted first-order logic with equality and no terms.
> But that's a trivial text error & doesn't take away the quality of the
> result.
>
> --- David A. Wheeler
>
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