Minimal Predicates, Fixed Points, and Definability
Johan van Benthem

Abstract:
We analyse the use of predicate minimization as a logical device,
determining the circumstances when it is appropriate in both semantic
and syntactic terms . Our main result here is a syntactic
characterization of all first-order formulas satisfying a semantic
property of predicate intersection. Moreover, we show how the use of
this device sheds new light on old issues of frame definability in
modal logic, leading to a semantic hierarchy of frame conditions with
a natural level of fixed-point definability in between first-order and
general higher-order.