Related papers: Mutually algebraic structures and expansions by pr…
Every bounded definable open set is a union of finitely many open strong cells in a weakly o-minimal expansion of a real closed field. We prove this fact and another theorem similar to it.
We study definable sets $D$ of SU-rank 1 in $M^{eq}$, where $M$ is a countable homogeneous and simple structure in a language with finite relational vocabulary. Each such $D$ can be seen as a `canonically embedded structure', which inherits…
We study structural limitations of purely algebraic reasoning in the analysis of arithmetic dynamical systems. Rather than addressing the truth of specific conjectures, we introduce a fragment - relative notion of algebraic refutability for…
We give characterizations of unital uniform topological algebras and saturated locally multiplicatively convex algebras by means of multiplicative linear functionals. Some automatic continuity theorems in advertibly complete uniform…
This work explores the deformation theory of algebraic structures in a very general setting. These structures include commutative, associative algebras, Lie algebras, and the infinity versions of these structures, the strongly homotopy…
We investigate a hierarchy of arithmetical structures obtained by a transfinite addition of a canonic universal predicate, where the canonic universal predicate for M is defined as a minimum universal predicate for M in terms of…
Based on the properties of the poset of those equivalence relations of a multialgebra for which the factor multialgebra is a universal algebra, we give a characterization for the fundamental relations of a multialgebra. We point out the…
For a complete, stable theory $T$ we construct, in a reasonably canonical way, a related stable theory $T^*$ which has higher independent amalgamation properties over the algebraic closure of the empty-set. The theory $T^*$ is an algebraic…
A natural construction of the logarithmic extension of the M(2,p) minimal models is presented, which generalises our previous model [0708.0802] of percolation (p=3). Its key aspect is the replacement of the minimal model irreducible modules…
In this paper we establish a general framework in which the verification of support theorems for generalized convex functions acting between an algebraic structure and an ordered algebraic structure is still possible. As for the domain…
We study the structure of infinite discrete sets D definable in expansions of ordered Abelian groups whose theories are strong and definably complete, with particular emphasis on the set D' comprised of differences between successive…
We prove that if A is a finite algebra with a parallelogram term that satisfies the split centralizer condition, then A is dualizable. This yields yet another proof of the dualizability of any finite algebra with a near unanimity term, but…
We develop a general axiomatic theory of algebraic pairs, which simultaneously generalizes several algebraic structures, in order to bypass negation as much as feasible. We investigate several classical theorems and notions in this setting…
We give a general account of family algebras over a finitely presented linear operad, this operad together with its presentation naturally defining an algebraic structure on the set of parameters.
Extending previous work, we define monoidal algebraic model structures and give examples. The main structural component is what we call an algebraic Quillen two-variable adjunction; the principal technical work is to develop the category…
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…
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…
Below, by space we mean a separable metrizable zero-dimensional space. It is studied when the space can be embedded in a Cantor set while maintaining the algebraic structure. Main results of the work: every space is an open retract of a…
An algebraic structure is said to be congruence permutable if its arbitrary congruences $\alpha$ and $\beta$ satisfy the equation $\alpha \circ \beta =\beta \circ \alpha$, where $\circ$ denotes the usual composition of binary relations. For…
We extend the theory (formal part only} of algebras with one binary operation (our paper arXiv:math/0110333v1 [math.RA] 31 Oct 2001) to algebras with several operations of any arity.