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Added
For a treatment in homotopy type theory see
- Dan Frumin, Herman Geuvers, Léon Gondelman, Niels van der Weide, Finite Sets in Homotopy Type Theory, (pdf)
Re-organised slightly. Added a brief introductory section, moved a couple of paragraphs of existing content into it. Removed the two context menus ’foundations’ and ’mathematics’ which I don’t think really fit here (the latter is arguably too general to be useful on any page).
Intend to add a new section in a subsequent edit.
Richard, maybe we can mention (in the “Viewing as schemes” section) that a finite coproduct of affine schemes $Spec R_i$, $i=1,\ldots,n$, is again affine, $Spec (R_1 \times \cdots \times R_n)$. Taking $R_i=\mathbb{Z}$, we can view the finite set $X$ as the (affine) scheme $Spec (\mathbb{Z}^X)$. This agrees with what you wrote, but seems more canonical.
Nice! Great if you can go ahead and make an edit if you have time, as I’ll be tied up until the evening European time!
Maybe keep the explicit description, but add the nice canonical one in addition?
Thanks for the edit!
Correction: not all finite subsets are decidable subsets. Any singleton in the real numbers is finite but generally not decidable unless the real numbers themselves have decidable equality. But finite subsets of sets with decidable equality are decidable subsets, and every finite set has decidable equality.
Owen Coyle
Thanks. I have touched the formatting and moved the item into chronological order (now here).
Also copied it to the author’s entries (at Arnaud Spiwack and Thierry Coquand).
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