An overview of nominal algebra, lattice, representation and dualities for computer science foundations
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Nominal algebra lets us axiomatise substitution and quantifiers, and thus
the newquantifier, firstorder logic, and the lambdacalculus. Nominal
lattice theory lets us characterise binders as greatest and least upper
bounds subject to freshness conditions; this is possible for “forall” and
“exists” and surprisingly also for “lambda”.
From this follow a body of soundness, completeness, representation, and
topological duality results for algebraic/latticetheoretic theories in
nominal sets and topological spaces. A great deal of structure is revealed
by this, which I will outline.
This talk is part of the Logic and Semantics Seminar (Computer Laboratory) series.
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