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On the Rigidity of Lattices of Topologies on Vector Spaces

期刊: ORDER-A JOURNAL ON THE THEORY OF ORDERED SETS AND ITS APPLICATIONS, 2023; ()

A vector topology on a vector space over a topological field is a (not necessarily Hausdorff) topology by which the addition and the scalar multiplica......

Big Ramsey Spectra of Countable Chains

期刊: ORDER-A JOURNAL ON THE THEORY OF ORDERED SETS AND ITS APPLICATIONS, 2023; 40 (2)

A big Ramsey spectrum of a countable chain (i.e. strict linear order) C is a sequence of big Ramsey degrees of finite chains computed in C. In this pa......

Representations for the Largest Extension of a Closure System

期刊: ORDER-A JOURNAL ON THE THEORY OF ORDERED SETS AND ITS APPLICATIONS, 2023; 40 (1)

An extension of a closure system on a finite set S is a closure system on the same set S containing the first one as a sublattice. A closure system ca......

On Finitely-Generated Johansson Algebras

期刊: ORDER-A JOURNAL ON THE THEORY OF ORDERED SETS AND ITS APPLICATIONS, 2023; 40 (2)

Kuznetsov's Theorem about finitely-generated Heyting algebras has been extended to Johansson algebras in the following way: if A = (A; boolean AND, bo......

The Dimension of Divisibility Orders and Multiset Posets

期刊: ORDER-A JOURNAL ON THE THEORY OF ORDERED SETS AND ITS APPLICATIONS, 2023; ()

The Dushnik-Miller dimension of a poset P is the least d for which P can be embedded into a product of d chains. Lewis and Souza isibility order on th......

Characteristic Polynomials of the Weak Order on Classical and Affine Coxeter Groups

期刊: ORDER-A JOURNAL ON THE THEORY OF ORDERED SETS AND ITS APPLICATIONS, 2023; ()

We find a simple product formula for the characteristic polynomial of the permutations with a fixed descent set under the weak order. As a corollary w......

A Study of the Small Inductive Dimension in the Area of Finite Lattices

期刊: ORDER-A JOURNAL ON THE THEORY OF ORDERED SETS AND ITS APPLICATIONS, 2023; ()

The Dimension Theory in the class of frames was the base of many researches. Especially, the covering dimension, the quasi covering dimension, the sma......

Antichains in the Bruhat Order for the Classes A(n, k)

期刊: ORDER-A JOURNAL ON THE THEORY OF ORDERED SETS AND ITS APPLICATIONS, 2023; ()

Let A(n, k) represent the collection of all n x n zero-and-one matrices, with the sum of all rows and columns equalling k. This set can be ordered by ......

A Study on Some Classes of Distributive Lattices with a Generalized Implication

期刊: ORDER-A JOURNAL ON THE THEORY OF ORDERED SETS AND ITS APPLICATIONS, 2023; ()

A generalized implication on a distributive lattice A is a function between A x A to ideals of A satisfying similar conditions to strict implication o......

The Minor Order of Homomorphisms via Natural Dualities

期刊: ORDER-A JOURNAL ON THE THEORY OF ORDERED SETS AND ITS APPLICATIONS, 2023; 40 (1)

We study the minor relation for algebra homomorphims in finitely generated quasivarieties that admit a logarithmic natural duality. We characterize th......

A Construction for Boolean Cube Ramsey Numbers

期刊: ORDER-A JOURNAL ON THE THEORY OF ORDERED SETS AND ITS APPLICATIONS, 2023; 40 (2)

Let Q(n) be the poset that consists of all subsets of a fixed n-element set, ordered by set inclusion. The poset cube Ramsey number R(Q(n), Q(n)) is d......

Gluing Residuated Lattices

期刊: ORDER-A JOURNAL ON THE THEORY OF ORDERED SETS AND ITS APPLICATIONS, 2023; 40 (3)

We introduce and characterize various gluing constructions for residuated lattices that intersect on a common subreduct, and which are subalgebras, or......

Extension of Sectional Pseudocomplementation in Posets

期刊: ORDER-A JOURNAL ON THE THEORY OF ORDERED SETS AND ITS APPLICATIONS, 2023; ()

Sectional pseudocomplementation (sp-complementation) on a poset is a partial operation * which associates with every pair (x, y) of elements, where x ......

A Proof of the Alternate Thomassé Conjecture for Countable N-Free Posets

期刊: ORDER-A JOURNAL ON THE THEORY OF ORDERED SETS AND ITS APPLICATIONS, 2023; ()

An N-free poset is a poset whose comparability graph does not embed an induced path with four vertices. We use the well-quasi-order property of the cl......

On Dually-CPT and Strongly-CPT Posets

期刊: ORDER-A JOURNAL ON THE THEORY OF ORDERED SETS AND ITS APPLICATIONS, 2023; ()

A poset is a containment of paths in a tree (CPT) if it admits a representation by containment where each element of the poset is represented by a pat......

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