By a nearlattice is meant a join-semilattice where every principal filter is a lattice with respect to the induced order. The aim of our paper is to show for which nearlattice and its element the mapping is a (surjective, injective) homomorphism of into .
We construct a totally ordered set Γ of positive infinite germs (i.e. germs of positive real-valued functions that tend to +∞), with order type being the lexicographic product ℵ1 × ℤ2. We show that Γ admits order preserving automorphisms of pairwise distinct growth rates.
Following the ideas of R. DeMarr, we establish a Galois connection between distance functions on a set and inequality relations on . Moreover, we also investigate a relationship between the functions of and .
The concept of a deductive system has been intensively studied in algebraic logic, per se and in connection with various types of filters. In this paper we introduce an axiomatization which shows how several resembling theorems that had been separately proved for various algebras of logic can be given unique proofs within this axiomatic framework. We thus recapture theorems already known in the literature, as well as new ones. As a by-product we introduce the class of pre-BCK algebras.
In [3] a metric on a system of isomorphism classes of ordered sets was defined. In this paper we define another metric on the same system and investigate some of its properties. Our approach is motivated by a problem from practice.
In the context of the atomic poset, we propose several new methods of constructing the complete lattice and the algebraic lattice, and the mutual decision of relationship between atomic posets and complete lattices (algebraic lattices) is studied.
In this paper, we establish a theorem on Möbius inversion over power set lattices which strongly generalizes an early result of Whitney on graph colouring.
Characterizations for a pseudocomplemented modular join-semilattice with 0 and 1 and its ideal lattice to be a Stone lattice are given.