 
Summary: FirstOrder Logical Duality
Henrik Forssell
A dissertation submitted in partial fulfillment of the
requirements for the degree of
PhD in Logic, Computation and Methodology
Carnegie Mellon University
2008
Abstract
Generalizing Stone duality for Boolean algebras, an adjunction between Bool
ean coherent categoriesrepresenting firstorder syntaxand certain topo
logical groupoidsrepresenting semanticsis constructed. The embedding
of a Boolean algebra into a frame of open sets of a space of 2valued mod
els is replaced by an embedding of a Boolean coherent category, B, into a
topos of equivariant sheaves on a topological groupoid of setvalued models
and isomorphisms between them. The latter is a groupoid representation
of the topos of coherent sheaves on B, analogously to how the Stone space
of a Boolean algebra is a spatial representation of the ideal completion of
the algebra, and the category B can then be recovered from its semantical
groupoid, up to pretopos completion. By equipping the groupoid of sets and
bijections with a particular topology, one obtains a particular topological
