Academic-turned-teacher (but still doing research as a hobby), interested in mathematical logic - specifically, computability theory and reverse mathematics, set theory, and abstract model theory. I'm also interested in other Nifty Things, in mathematics and elsewhere.
Since the SE system only allows temporary bounties, I am here informally "perma-bountying" the following ten questions, each for 1000 points (only a complete answer is guaranteed the bounty, so e.g. a partial answer to the unraveling question within the next week probably would get the standard 500-point bounty currently offered but probably would not get a further +500 reward):
Geometry and topology:
involutive triangle centers
axiomatized function spaces
Model theory:
ultrapowers and automorphisms
second-order Tarski-Vaughtification
Descriptive set theory:
unraveling and determinacy
Banach game quantifier
Set theory:
gently changing measure
second-order properties and ultrafilters
Computability theory:
strong +1 hypothesis
cone property and e-degrees