We prove that if X,X are closed subschemes of a torus T over a non-Archimedean field K, of complementary codimension and with finite intersection, then the stable tropical intersection along a (possibly positive-dimensional, possibly unbounded) connected componentC of Trop(X)∩Trop(X) lifts to algebraic intersection points, with multiplicities. This theorem requires potentially passing to a suit...

Intersection results for families of H-convex sets in H-spaces are given. These extend known results concerning families of convex sets in topological vector spaces, such as the Berge-Klee intersection theorem and a previous result of the author. MSC 2000. 52A01, 14E20.

“ This paper defines reduction on derivations (cut-elimination) in the Strict Intersection Type Assignment System of [1] and shows a strong normalisation result for this reduction. Using this result, new proofs are given for the approximation theorem and the characterisation of normalisability of terms, using intersection types. ”

‎for a set of non-negative integers~$l$‎, ‎the $l$-intersection number of a graph is the smallest number~$l$ for which there is an assignment of subsets $a_v subseteq {1,dots‎, ‎l}$ to vertices $v$‎, ‎such that every two vertices $u,v$ are adjacent if and only if $|a_u cap a_v|in l$‎. ‎the bipartite $l$-intersection number is defined similarly when the conditions are considered only for the ver...

In this paper, we relate the problem of finding a maximum clique to the intersection number of the input graph (i.e. the minimum number of cliques needed to edge cover the graph). In particular, we consider the maximum clique problem for graphs with small intersection number and random intersection graphs (a model in which each one of m labels is chosen independently with probability p by each ...

Reny and Wooders (1998) showed that there is some point in the intersection of sets in Shapley’s (1973) generalization of the Knaster-Kuratowski-Mazurkiwicz Theorem with the property that the collection of all sets containing that point is partnered as well as balanced. We provide a further extension by showing that the collection of all such sets can be chosen to be strictly balanced, implying...

In simply typed λ-calculus with one ground type the following theorem due to Loader holds. (i) Given the full model F over a finite set, the question whether some element f ∈ F is λ-definable is undecidable. In the λ-calculus with intersection types based on countably many atoms, the following is proved by Urzyczyn. (ii) It is undecidable whether a type is inhabited. Both statements are major r...

10. Galois modules and class field theory Boas Erez In this section we shall try to present the reader with a sample of several significant instances where, on the way to proving results in Galois module theory, one is lead to use class field theory. Conversely, some contributions of Galois module theory to class fields theory are hinted at. We shall also single out some problems that in our op...

The purpose of this article is to point out a mistake in the published paper Graphs hyperbolic groups and limit set intersection theorem- Proc AMS, vol 146, no 5, pp 1859--1871, which subsequently weakens main theorem that paper. We state prove weaker result note.

One of the fundamental results regarding intersection bodies is Busemann’s theorem, which states that the intersection body of a symmetric convex body is convex. Thus, it is natural to ask how much of convexity is guaranteed under the intersection body operation. In this paper we provide several results about the (strict) improvement of convexity for intersection bodies of symmetric bodies of r...