相关论文: Arities and aritizabilities of first-order theorie…

We study links between first-order formulas and arbitrary properties for families of theories, classes of structures and their isomorphism types. Possibilities for ranks and degrees for formulas and theories with respect to given properties…

We introduce a notion of Pre-structurable Algebras based upon triality relations and study its relation to structurable algebra of Allison, as well as to Lie algebras satisfying triality.

We introduce the notion of limiting theories, giving examples and providing a sufficient condition under which the first order theory of a structure is the limit of the first order theories of a collection of substructures. We also give a…

Classification theory of elementary classes deals with first order (elementary) classes of structures (i.e. fixing a set T of first order sentences, we investigate the class of models of T with the elementary submodel notion). It tries to…

Monads are of interest both in semantics and in higher dimensional algebra. It turns out that the idea behind usual notion finitary monads (whose values on all sets can be computed from their values on finite sets) extends to a more general…

We introduce the calculus of neo-Peircean relations, a string diagrammatic extension of the calculus of binary relations that has the same expressivity as first order logic and comes with a complete axiomatisation. The axioms are obtained…

We study possibilities for almost $n$-ary and $n$-aritizable theories. Their dynamics both in general case, for $\omega$-categorical theories, and with respect to operations for theories are described.

We announce a number of conjectures associated with and arising from a study of primes and irrationals in $\mathbb{R}$. All are supported by numerical verification to the extent possible.

We study approximations of theories both in general context and with respect to some natural classes of theories. Some kinds of approximations are considered, connections with finitely axiomatizable theories and minimal generating sets of…

Work in progress concerning alternative formalizations of arithmetic.

We show that the decidability of the first-order theory of the language that combines Boolean algebras of sets of uninterpreted elements with Presburger arithmetic operations. We thereby disprove a recent conjecture that this theory is…

First order formulas in a relational signature can be considered as operations on the relations of an underlying set, giving rise to multisorted algebras we call first order algebras. We present universal axioms so that an algebra satisfies…

Analytical thinking is dominated by binary ideas. From pair-wise interactions, to algebraic operations, to compositions of processes, to network models, binary structures are deeply ingrained in the fabric of most current scientific…

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.

Theory of Riemann Extensions of the spaces with constant affine connection for the studying of the properties of nonlinear the first order systems of differential equations is proposed. Quadratic planar system of equations and the Lorenz…

This article develops a comprehensive theory of multiary graded polyadic algebras, extending the classical concept of group-graded algebras to higher-arity structures. We introduce the notion of grading by multiary groups and investigate…

We use model theoretic techniques to construct explicit first-order axiomatizations for the classes of posets that can be represented as systems of sets, where the order relation is given by inclusion, and existing meets and joins of…

We define a notion which contains numerous basic notions of Analysis as special cases, for example limit, continuity, differential, Riemann and Lebesgue integral, root and exponential functions. Properties like additivity or linearity of…

We study applications of a general approach for arities and arizabilities of theories to group and monoid theories. It is proved that a theory of a group $G$ is aritizable if and only if $G$ is finite. It is shown that this criterion does…

A general theory of the Frolicher-Nijenhuis and Schouten-Nijenhuis brackets in the category of modules over a commutative algebra is described. Some related structures and (co)homology invariants are discussed, as well as applications to…