Related papers: A constructive Galois connection between closure a…
Generalizing the $\omega$-categorical context, we introduce a notion, which we call the Lascar Property, that allows for a fine analysis of the topological isomorphisms between automorphism groups of countable structures satisfying this…
In this article, we prove infinitary version of one to one correspondence theorem between clones and relational clones on a fixed possibly infinite set. We also characterize the relational clone corresponding to the clone of all finitary…
In this paper, we study some properties of the closure operator in the Mac\'ias topology on infinite integral domains. Moreover, under certain conditions, we present topological proofs of the infiniteness of maximal ideals and…
Two adjoint functors can be seen as generalisations of the two functions within a Galois connection. If instead the adjoints are not generalised from functions, but from relations, then analogously the object of study becomes a more general…
This article is a survey of closure operations on ideals in commutative rings, with an emphasis on structural properties and on using tools from one part of the field to analyze structures in another part. The survey is broad enough to…
The regular subgroup determining an induced Hopf Galois structure for a Galois extension $L/K$ is obtained as the direct product of the corresponding regular groups of the inducing subextensions. We describe here the associated Hopf algebra…
A Galois connection between clones and relational clones on a fixed finite domain is one of the cornerstones of the so-called algebraic approach to the computational complexity of non-uniform Constraint Satisfaction Problems (CSPs). Cohen…
Calculational abstract interpretation, long advocated by Cousot, is a technique for deriving correct-by-construction abstract interpreters from the formal semantics of programming languages. This paper addresses the problem of deriving…
A Galois correspondence theorem is proved for the case of inverse semigroups acting orthogonally on commutative rings as a consequence of the Galois correspondence theorem for groupoid actions. To this end, we use a classic result of…
In this article, we realize some groups as Galois groups over rational numbers and finite extension of rational numbers by studying right splitting of some exact sequences, Galois correspondence and algebraic operations on Galois…
The aim of this article is to give practicing teachers an overview about the theory behind paperfolding, it is my qualifying thesis(Zulassungsarbeit) as a teacher in Germany. It is a survey about the relations between paperfolding and…
We show that intuitionistic logic is deductively equivalent to Connexive Heyting Logic (CHL), hereby introduced as an example of a strong connexive logic with intuitive semantics. We use the reverse algebraisation paradigm: CHL is presented…
An algebraic technique is presented that does not use results of model theory and makes it possible to construct a general Galois theory of arbitrary nonlinear systems of partial differential equations. The algebraic technique is based on…
In the preprint we present an outline of the one dimensional version of topological Galois theory. The theory studies topological obstruction to solvability of equations "in finite terms" (i.e. to their solvabilty by radicals, by elementary…
The general Galois theory for functions and relational constraints over arbitrary sets described in the authors' previous paper is refined by imposing algebraic conditions on relations.
Classical logic is embedded into constructive logic, through a definition of the classical connectives and quantifiers in terms of the constructive ones.
The Bourgeois construction associates to every contact open book on a manifold $V$ a contact structure on $V\times T^2$. We study in this article some of the properties of $V$ that are inherited by $V\times T^2$ and some that are not.…
Three classes of models of QHC, the joint logic of problems and propositions, are constructed, including a class of subset/sheaf-valued models that is related to solutions of some actual problems (such as solutions of algebraic equations).…
Abstract axiomatic formulation of mathematical structures are extensively used to describe our physical world. We take here the reverse way. By making basic assumptions as starting point, we reconstruct some features of both geometry and…
After an overview of noncommutative differential calculus, we construct parts of it explicitly and explain why this construction agrees with a fuller version obtained from the theory of operads.