We present a first order formula characterizing the distributive lattices L whose Priestley spaces P(L) contain no copy of a finite forest T . For Heyting algebras L, prohibiting a finite poset T in P(L) is characterized by equations iff T is a tree. We also give a condition characterizing the distributive lattices whose Priestley spaces contain no copy of a finite forest with a single addition...

Let D be the system of all distributive lattices and let D0 be the system of all L ∈ D such that L possesses the least element. Further, let D1 be the system of all infinitely distributive lattices belonging to D0. In the present paper we investigate the radical classes of the systems D, D0 and D1.

A distributive lattice L with 0 is finitary if every interval is finite. A function f : N0 N0 is a cover function for L if every element with n lower covers has f (n) upper covers. In this paper, all finitary distributive lattices with non-decreasing cover functions are characterized. A 1975 conjecture of Richard P. Stanley is thereby settled. 2000 Academic Press

A discrete Sugeno integral on a bounded distributive lattice L is defined as an idempotent weighted polynomial. Another possibility for axiomatization of integrals to consider compatible aggregation functions, uniquely extending the L-valued fuzzy measures. This paper aims study mentioned unique extension property concerning possible non-distributive lattices. We show that this equivalent distr...

A simple proof is given of Chen's and Grätzer's theorem, which gives a method to construct a Stone algebra from a Boolean algebra and a distributive lattice with 1 by certain connective conditions between the two given lattices. C. C. Chen and G. Grätzer [1] proved originally the Construction Theorem for Stone algebras. In [3] we proved by different method the Construction Theorem for a larger ...

In this paper, the concepts of L-concave structures, concave Linterior operators and concave L-neighborhood systems are introduced. It is shown that the category of L-concave spaces and the category of concave Linterior spaces are isomorphic, and they are both isomorphic to the category of concave L-neighborhood systems whenever L is a completely distributive lattice. Also, it is proved that th...

We provide an extension of the notion of chain-valued frame introduced by Pultr and Rodabaugh in [Category theoretic aspects of chain-valued frames: parts I and II, Fuzzy Sets and Systems 159 (2008) 501–528 and 529–558] by relaxing the assumption that L be a complete chain. As a result of this investigation we formulate the category L-Frm of L-frames under the weaker assumption that L is a comp...

Every N „-categorical distributive lattice of finite breadth has a finitely axiomatizablc theory. This result extends the analogous result for partially ordered sets of finite width. 0. Introduction. This note is mainly concerned with the following theorem. Theorem 1. Every S „-categorical distributive lattice of finite breadth has a finitely axiomatizable theory. For general references on dist...

in this paper, the concept of countably near ps-compactness inl-topological spaces is introduced, where l is a completely distributive latticewith an order-reversing involution. countably near ps-compactness is definedfor arbitrary l-subsets and some of its fundamental properties are studied.

A distributive lattice L with 0 is finitary if every interval is finite. A function f : N0 ! N0 is a cover function for L if every element with n lower covers has f ðnÞ upper covers. All non-decreasing cover functions have been characterized by the author ([2]), settling a 1975 conjecture of Richard P. Stanley. In this paper, all finitary distributive lattices with cover functions are character...