Representation of order automorphisms by words.
Representation of ordered classes by classes of connected unary algebras
Représentations indécomposables des ensembles ordonnés
Representations of bipartite completed posets.
Representations of locally distributive lattices
Representative properties of the quasi-ordered set
Residuation in twist products and pseudo-Kleene posets
M. Busaniche, R. Cignoli (2014), C. Tsinakis and A. M. Wille (2006) showed that every residuated lattice induces a residuation on its full twist product. For their construction they used also lattice operations. We generalize this problem to left-residuated groupoids which need not be lattice-ordered. Hence, we cannot use the same construction for the full twist product. We present another appropriate construction which, however, does not preserve commutativity and associativity of multiplication....
Restricted ideals and the groupability property. Tools for temporal reasoning
In the field of automatic proving, the study of the sets of prime implicants or implicates of a formula has proven to be very important. If we focus on non-classical logics and, in particular, on temporal logics, such study is useful even if it is restricted to the set of unitary implicants/implicates [P. Cordero, M. Enciso, and I. de Guzmán: Structure theorems for closed sets of implicates/implicants in temporal logic. (Lecture Notes in Artificial Intelligence 1695.) Springer–Verlag, Berlin 1999]....
Resultats sur la comparaison des types d΄ordres
Retract extensions of ordered sets.
Riduzioni omotopicamente invarianti di insiemi parzialmente ordinati
Ring-like operations is pseudocomplemented semilattices
Ring-like operations are introduced in pseudocomplemented semilattices in such a way that in the case of Boolean pseudocomplemented semilattices one obtains the corresponding Boolean ring operations. Properties of these ring-like operations are derived and a characterization of Boolean pseudocomplemented semilattices in terms of these operations is given. Finally, ideals in the ring-like structures are defined and characterized.
Ring-like structures derived from -lattices with antitone involutions
Using the concept of the -lattice introduced recently by V. Snášel we define -lattices with antitone involutions. For them we establish a correspondence to ring-like structures similarly as it was done for ortholattices and pseudorings, for Boolean algebras and Boolean rings or for lattices with an antitone involution and the so-called Boolean quasirings.
Rotations of -lattices
In [2], J. Klimes studied rotations of lattices. The aim of the paper is to research rotations of the so-called -lattices introduced in [3] by V. Snasel.
Sacks forcing collapses to
We shall prove that Sacks algebra is nowhere -distributive, which implies that Sacks forcing collapses to .
Selfduality of the system of convex subsets of a partially ordered set
For a partially ordered set let us denote by the system of all convex subsets of . It is found the necessary and sufficient condition (concerning ) under which (as a partially ordered set) is selfdual.
Selfduality of the system of intervals of a partially ordered set
Semi-closure mappings and cofinal chains
Semigroups of order-decreasing transformations: the isomorphism theorem.
Semigroups of order-preserving partial endomorphisms on trees, I