A game on a convex geometry is a real-valued function de0ned on the family L of the closed sets of a closure operator which satis0es the 0nite Minkowski–Krein–Milman property. If L is the boolean algebra 2 then we obtain an n-person cooperative game. Faigle and Kern investigated games where L is the distributive lattice of the order ideals of the poset of players. We obtain two classes of axiom...

In this paper we investigate weak contact relations C on a lattice L, in particular, the relation between various axioms for contact, and their connection to the algebraic structure of the lattice. Furthermore, we will study a notion of orthogonality which is motivated by a weak contact relation in an inner product space. Although this is clearly a spatial application, we will show that, in cas...

Based on an acyclic orientation of the Z-transformation graph, a finite distributive lattice (FDL for short)M(G) is established on the set of all 1-factors of a plane (weakly) elementary bipartite graph G. For an FDL L, if there exists a plane bipartite graph G such that L is isomorphic to M(G), then L is called a matchable FDL. A natural question arises: Is every FDL a matchable FDL? In this p...

A NOTE ON SUBMODULAR FUNCTIONS ON DISTRIBUTIVE LATTICES Satoru Fujishige University of Tsukuba Nobuaki Tomizawa Niigata University (Received July 15, 1982; Rllvised June 14, 1983) Let D be a distributive lattice formed by subsets of a finite set E with 1/>, E E D and let R be the set of reals. Also let f be a submodular function from D into R with f(l/» = O. We determine the set of extreme poin...

This thesis presents a series of theoretical results and practical realisations about the theory of computation in distributive categories. Distributive categories have been proposed as a foundational tool for Computer Science in the last years, starting from the papers of R.F.C. Walters. We shall focus on two major topics: distributive computability, i.e., a generalized theory of computability...

A category with finite products and finite coproducts is said to be distributive if the canonical map A×B + A×C → A× (B + C) is invertible for all objects A, B, and C. Given a distributive category D , we describe a universal functor D → Dex preserving finite products and finite coproducts, for which Dex is extensive; that is, for all objects A and B the functor Dex/A × Dex/B → Dex/(A + B) is a...

Remarkable cardinals were introduced by Schindler, who showed that the existence of a remarkable cardinal is equiconsistent with the assertion that the theory of L(R) is absolute for proper forcing [Sch00]. Here, we study the indestructibility properties of remarkable cardinals. We show that if κ is remarkable, then there is a forcing extension in which the remarkability of κ becomes indestruct...

Given a ∨ -complete (semi)lattice L, we consider L-labeled transition systems as coalgebras of a functor L(−), associating with a set X the set LX of all L-fuzzy subsets. We describe simulations and bisimulations of L-coalgebras to show that L(−) weakly preserves nonempty kernel pairs iff it weakly preserves nonempty pullbacks iff L is join infinitely distributive (JID). Exchanging L for a comm...