Related papers: Characterizing model completeness among mutually a…
We give a polymorphic account of the relational algebra. We introduce a formalism of ``type formulas'' specifically tuned for relational algebra expressions, and present an algorithm that computes the ``principal'' type for a given…
We define and study structural properties of hypergraphs of models of a theory including lattice ones. Characterizations for the lattice properties of hypergraphs of models of a theory, as well as for structures on sets of isomorphism types…
In this note we study associative dialgebras proving that the most interesting such structures arise precisely when the algebra is not semiprime. In fact the presence of some "perfection" property (simpleness, primitiveness, primeness or…
A structure M is pregeometric if the algebraic closure is a pregeometry in all M' elementarily equivalent to M. We define a generalisation: structures with an existential matroid. The main examples are superstable groups of U-rank a power…
Due to the increased complexity of software development projects more and more systems are described by models. The sheer size makes it impractical to describe these systems by a single model. Instead many models are developed that provide…
We provide a diagrammatic criterion for the existence of an absolute colimit in the context of enriched category theory.
We address the question of finding algebraic properties that are respectively equivalent, for a morphism between algebraic varieties over an algebraically closed field of characteristic zero, to be an homeomorphism for the Zariski topology…
A deductive system is structurally complete if its admissible inference rules are derivable. For several important systems, like modal logic S5, failure of structural completeness is caused only by the underivability of passive rules, i.e.…
We look at equivalence relations on the set of models of a theory -- MERs, for short -- such that the class of equivalent pairs is itself an elementary class, in a language appropriate for pairs of models. We provide many examples of…
A problem of completing a linear map on C*-algebras to a completely positive map is analyzed. It is shown that whenever such a completion is feasible there exists a unique minimal completion. This theorem is used to show that under some…
Motivated by the remarkable interplay between (chordal) graphs and matrix algebra, we associate to each graph a so-called completion number that might encode some aspects of that interplay. We show that this number is not trivial, and we…
We can define the adjacency algebra of an association scheme over arbitrary field. It is not always semisimple over a field of positive characteristic. The structures of adjacency algebras over a field of positive characteristic have not…
We show that the theory of De Morgan algebras has a model completion and axiomatise it. Then we prove that it is $\aleph_0$-categorical and describe definable and algebraic closures in that theory. We also obtain similar results for…
Universal algebraic geometry allows considering of geometric properties of every universal algebra. When two algebras have same algebraic geometry? We must consider the categories of algebraic closed sets of these algebras to answer this…
Over a field of characteristic zero we prove two formality conditions. We prove that a dg Lie algebra is formal if and only if its universal enveloping algebra is formal. We also prove that a commutative dg algebra is formal as a dg…
It is shown how regular model sets can be characterized in terms of regularity properties of their associated dynamical systems. The proof proceeds in two steps. First, we characterize regular model sets in terms of a certain map $\beta$…
We characterize characteristic polynomials of elements in a central simple algebra. We also give an account for the theory of rational canonical forms for separable linear transformations over a central division algebra, and a description…
For any minor-closed class of matroids over a fixed finite field, we state an exact structural characterization for the sufficiently connected matroids in the class. We also state a number of conjectures that might be approachable using the…
In this work we study the notions of structural and universal completeness both from the algebraic and logical point of view. In particular, we provide new algebraic characterizations of quasivarieties that are actively and passively…
Semifields are semirings in which every nonzero element has a multiplicative inverse. A rough classification uses the characteristic of the semifield, that is the isomorphism type of the semifield generated by the two neutral elements. For…