#freakypost

And the sound when leather jackets hit the ground

(cw suggestive, eyestrain)

I've been overthinking this hard. What structures count as algebraic, which have analytic or other structure to them? But oh well.

For an individual structure, I would have to say the surreal numbers. On a first algebraic glance, they're just an real closed field (which are already pretty cool), but they have tons of extra structure, like their tree structure coming from the notion of simplicity. They contain all the reals and all the ordinals, so "all numbers great and small". Also they're really vast - every ordered field embeds into them! The relevant technical notions here are "saturation" and "homogeneity", and the surreals seem to have that for everything you can view them as - as a linear order, as an exponential field, as some field of transseries... This makes them seem quite interesting for model theory, which I guess is what I mostly do these days. ^^