There are versions of Tarski’s axioms for synthetic Euclidean geometry that apply for any finite dimension $n \in \mathbb{N}$.

Anonymous

]]>Thanks!

]]>Removed now. Think there is a little bug in such cases, which submitting an edit after the first one usually solves. I’ll try to fix the bug when I get a chance.

]]>I’m trying again, have removed the redirect, but synthetic homotopy theory still ends up at synthetic mathematics

]]>Redirected from “synthetic homotopy theory”

Oh, I see. All the better! Let’s create that page, when anyone finds the time.

]]>Sorry that was me. I was in the process of setting up a new page yesterday, but removing the redirect didn’t generate the usual ? link, and I got called away. I’ll see if I have time today.

]]>I noticed that the link “synthetic homotopy theory” didn’t go anywhere. Have made it a redirect to *synthetic mathematics* now, since that is the entry which has a subsection “Synthetic homotopy theory”. Optimally it should be given it’s own entry, though.

added pointer to

- Egbert Rijke,
*Classifying Types*(arXiv:1906.09435)

Since “synthetic homnotopy theory” redirects here, I tried to add some pointers, but just a start:

Discussion of *synthetic homotopy theory* (typically understood as homotopy type theory):

Ulrik Buchholtz, Sec. 3.1 of

*Higher Structures in Homotopy Type Theory*(arXiv:1807.02177)Mike Shulman, slides 37 onwards in

*Homotopical trinitarianism:A perspective on homotopy type theory*, 2018 (pdf)

felt the desire to have an entry on the general idea (if any) of *synthetic mathematics*, cross-linking with the relevant examples-entries.

This has much room for being further expanded, of course.

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