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Oct 23 at 17:50 comment added YKY @Emily 100%. Thanks, it looks like I missed a lot of important development... but the thesis provides other references.
Oct 23 at 14:50 comment added Zhen Lin The old way of algebra-ising first-order logic is with cylindric algebras, but probably people prefer to think about Lawvere hyperdoctrines these days.
Oct 23 at 14:33 comment added Andreas Blass The spectrum of a Boolean ring is usually called (by people other than algebraic geometers) the Stone space of the ring. This representation of arbitrary Boolean rings as rings of sets was proved by M. Stone in the 1930's. Googling "Stone space" should produce plenty of references about this (and generalizations).
Oct 23 at 11:19 comment added Emily Maybe Spencer Breiner's thesis, Scheme representation for first-order logic, could be relevant.
Oct 23 at 10:00 history asked YKY CC BY-SA 4.0