Obstacles to Duality between Classes of Relational Structures
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We prove an algebraic result concerning inverse limits of copowers in anS-class of relational structures of the same (finitary or infinitary) type. Among several applications to the nonexistence of category dualities is the following Theorem: If there exist arbitrarily large measurable cardinals then any classK of relational structures containing a nontrivial objectA and all of its cartesian powers via nonempty index sets will fail to be dual to anyS-class. (No large cardinal assumption is necessary if either there is a finite suchA or ifK consists only of finitary relational structures and contains the elementary class generated byA and its cartesian powers).
Bankston, Paul, "Obstacles to Duality between Classes of Relational Structures" (1983). Mathematics, Statistics and Computer Science Faculty Research and Publications. 171.