A note on bounded arithmetic
0. Introduction. Besides being of intrinsic interest, cylindric (semi-) lattices arise naturally from the study of dependencies in relational databases; the polynomials on a cylindric semilattice are closely related to the queries obtainable from project-join mappings on a relational database (cf. [D] for references). This note is intended to initiate the study of these structures, and only a few, rather basic results will be given. Some problems at the end will hopefully stimulate further research....
Solecki has shown that a broad natural class of ideals of compact sets can be represented through the ideal of nowhere dense subsets of a closed subset of the hyperspace of compact sets. In this note we show that the closed subset in this representation can be taken to be closed upwards.