The class of supermodular functions on the power set of a non-empty nite set N forms a cone. It can be viewed as the direct sum of a linear subspace and of a cone of standardized supermodular functions which has nitely many extreme rays. Every extreme ray can be described by a standardized integer-valued set function. We analyse the situation in the case when N has ve elements (= variables). A ...

An Ockham algebra L = (L,∧,∨, f, 0, 1) that satisfies the identity f2n+m = fm, n ∈ N and m ∈ N0, is called a Kn,m-algebra. Generalizing some results obtained in [2], J. Varlet and T. Blyth, in [3, Chapter 8], study congruences on K1,1-algebras. In particular, they describe the complement (when it exists) of a principal congruence and characterize these congruences that are complemented. In this...

We prove how any (elementary) topos may be reconstructed from the data of two complemented subtoposes together with a pair of left exact “glueing functors”. This generalizes the classical glueing theorem for toposes, which deals with the special case of an open subtopos and its closed complement. Our glueing analysis applies in a particularly simple form to a locally closed subtopos and its com...