Re: Stupid question: what space was Euclid working in?

Vaughan Pratt writes:

Regarding Bob Knighten's question on approaches to synthetic Euclidean geometry such as Hilbert's axiomatization, has anyone axiomatized more than E_3 (Euclid Books 11-13)? A satisfactory definition of Euclidean space needs to account for all finite dimensions.

Postings crossing in the ether make this a bit confusing, but Toby Bartels effectively answered this with his reference to Tarski's axioms so my only additional contribution is a reference where the details for all finite dimensions are discussed: Alfred Tarski and Givant, Steven, 1999, "Tarski's system of geometry," Bulletin of Symbolic Logic 5: 175-214. -- Bob -- Robert L. Knighten RLK@knighten.org