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I have cross-linked the quadruple of entries
Euclidean geometry, Klein geometry
Riemannian geometry, Cartan geometry
and briefly edited the entries otherwise. For instance added an Idea-sentence to Euclidean geometry, and expanded Klein geometry (for instance the Examples).
There is no entry Riemann geometry, possibly Riemannian geometry.
thanks, fixed.
At Euclidean geometry, a new batch of material on axiomatizations, including a discussion on Tarski’s geometry.
Thanks. I have added mentioning of the word synthetic geometry here
Stupid question regarding the statement that “Hilbert’s theory is categorical”: is there are any chance that one could say “is categoric” ?? To avoid the clash of terminology (at least of associations).
Have people given more obviously type theoretic renditions of geometries such as the Euclidean one? I could imagine advantages to having more than Tarski’s single sort.
In the projective case, I guess we’d see the duality symmetry of exchanging the line and point types.
Urs #6: I’d not heard that suggestion before. Toby is one of those who advise category theorists to say “categorial” for their own meaning instead of “categorical”, to avoid this clash. I don’t like this much personally; something about it seems too subservient to model theory (I would guess mathematicians say “categorical” in the, um, categorical sense much more often than in the model-theoretic sense).
Honestly, I don’t mind inventing a new word for the purposes of the nLab. If someone edits in “categoric” with a link, I won’t say a thing. Either way I’ll be at peace. :-)
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