Powerset operators and selection principles
by
Cosimo Guido
Department of Mathematics, University of Lecce
Coauthors: Elena Musio, Paola Toto

Powerset operators associated to functions between sets are considered and their lattice theoretical properties are remarked, mainly, for the second order case. These seems to give a useful tool for studying invariance of selection principles and partition relations under maps, yet in the classical case of subsets with characteristic function taking values in the trivial lattice {0, 1}. Moreover the powerset-operators approach promises to be the main way for considering selection principles and combinatorics of covers in non-classical set theories. A few results and directions are outlined in the application of the properties of powerset operators to selection principles.

Date received: November 30, 2005