A note on cofinal extensions and segments
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.
We generalize the theory of generic subsets of definably compact definable groups to arbitrary o-minimal structures. This theory is a crucial part of the solution to Pillay's conjecture connecting definably compact definable groups with Lie groups.
Pseudo BL-algebras are a noncommutative extention of BL-algebras. In this paper we study good pseudo BL-algebras and consider some classes of these algebras.