Related papers: Constructing many atomic models in $\aleph_1$
We study invariant pseudo-K\"ahler structures on a solvmanifold $G$ such that the Lie algebra $\mathfrak{g}$ is almost abelian, that is $\mathfrak{g}=\mathfrak{h}\rtimes\mathbb{R}$, with $\mathfrak{h}$ abelian; comparing with the…
We classify strongly homotopy Lie algebras - also called L-infinity algebras - of one even and two odd dimensions, which are related to $2|1$-dimensional $Z_2$-graded Lie algebras. What makes this case interesting is that there are many…
The purpose of the present paper is to show that: Eilenberg-type correspondences = Birkhoff's theorem for (finite) algebras + duality. We consider algebras for a monad T on a category D and we study (pseudo)varieties of T-algebras.…
We streamline treatments of the interpretability orders $\trianglelefteq^*_\kappa$ of Shelah, the key new notion being that of pseudosaturation. Extending work of Malliaris and Shelah, we classify the interpretability orders on the stable…
A generalized pseudo effect algebra (GPEA) is a partially ordered partial algebraic structure with a smallest element 0, but not necessarily with a unit (i.e, a largest element). If a GPEA admits a so-called unitizing automorphism, then it…
We study the problem of modeling a binary operation that satisfies some algebraic requirements. We first construct a neural network architecture for Abelian group operations and derive a universal approximation property. Then, we extend it…
We define cohomology of associative H-pseudoalgebras, and we show that it describes module extensions, abelian pseudoalgebra extensions, and pseudoalgebra first order deformations. We describe in details the same results for the special…
The paper is devoted to classification problem of finite dimensional complex none Lie filiform Leibniz algebras. The motivation to write this paper is an unpublished yet result of J.R.Gomez, B.A.Omirov on necessary and sufficient conditions…
We prove that for every tower $\mathcal T$ there are $\aleph_1$-dense $A$ and $B$ so that any ``reasonable" forcing notion $\mathbb{P}$ -- an adjective that includes all known ones -- for making $A$ and $B$ isomorphic will add a…
We give a unified treatment of the model theory of various enrichments of infinite atomic Boolean algebras, with special attention to quantifier-eliminations, complete axiomatizations and decidability. A classical example is the enrichment…
We study algorithmic randomness notions via effective versions of almost-everywhere theorems from analysis and ergodic theory. The effectivization is in terms of objects described by a computably enumerable set, such as lower semicomputable…
An algebra ${\cal G}$ of symmetric {\em one-particle} operators is constructed for the Calogero model. This is an infinite-dimensional Lie-algebra, which is independent of the interaction parameter $\lambda$ of the model. It is constructed…
A rigorous mathematical theory of dimensional analysis, systematically accounting for the use of physical quantities in science and engineering, perhaps surprisingly, was not developed until relatively recently. We claim that this has…
We study the implications of model completeness of a theory for the effectiveness of presentations of models of that theory. It is immediate that for a computable model $\mathcal A$ of a computably enumerable, model complete theory, the…
The notions of module pseudo-amenable and module pseudo-contractible Banach algebras are introduced. For a Banach algebra with bounded approximate identity, module pseudo-amenability and module approximate amenability are the same…
Given a first-order sentence, a model-checking computation tests whether the sentence holds true in a given finite structure. Data provenance extracts from this computation an abstraction of the manner in which its result depends on the…
In this paper we study the lengths of certain chains of subalgebras of a Lie algebra L: namely, a chief series, a maximal chain of minimal length, a chain of maximal length in which each subalgebra is modular in L, and a chain of maximal…
We survey both old and new developments in the theory of algorithms in real algebraic geometry -- starting from effective quantifier elimination in the first order theory of reals due to Tarski and Seidenberg, to more recent algorithms for…
The package fhi98PP allows one to generate norm-conserving pseudopotentials adapted to density-functional theory total-energy calculations for a multitude of elements throughout the periodic table, including first-row and transition metal…
Algebraic hyperstructures represent a natural extension of classical algebraic structures. In a classical algebraic structure, the composition of two elements is an element, while in an algebraic hyperstructure, the composition of two…