Update on Undecidable “Elementary” Geometry

I mentioned a few weeks ago that I had trouble locating upper- and lower-dimensional axioms for Tarski's system. You can find examples in this presentation. On the other hand, I prefer mine.

As for devising a plausible way to express spirals, I have run into a problem. Whenever I try thinking too hard about lines, circles, and spirals, the theme song for The Thomas Crown Affair keeps going through my head and interfering…