Re: hyperdoctrines and cylindric algebras

[Thomas Streicher <streicher@mathematik.tu-darmstadt.de>]

Couldn't one say that cylindric (and polyadic) algebras are awkward (from a
categorical point of view) formulations of posetal hyperdoctrines over
FinSet^op whose fibres are boolean algebras. So the pet objects of the
algebraic logicians are certain *presentations* of particular hyperdoctrines.
All this was worked out in a couple of papers by A. Daigneault beginning
of 70ies.
There is a lot of work by the algebraic logicians which I am not too familiar
with. There arises the question whether their work is of any use for questions
naturally arising to the categorical logician. That's how I understood Alex'
question and what I'd like to know myself.
Halmos was one of the first working on algebraic logic in the 50ies (polyadic
algebras) and was later positive w.r.t. categorical logic. That's what I have
heard of. Did he consider categorical logic as the "right formulation" of his
original aims? Maybe senior categorists do know about this?

Thomas