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Universal Logic: Evolution of a Project
We discuss the origin and development of the universal logic project. We describe in particular the structure of UNILOG, a series of events created...
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Bjarni Jónsson’s contributions in algebra: an addendum
This note is an addendum to clarify credit for universal relational systems and their properties.
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Simpler Maltsev conditions for (weak) difference terms in locally finite varieties
This paper is motivated by a practical question: given a finite algebra A in a finite language, how can we best program a computer to decide whether...
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Ultraproducts preserve finite subdirect reducibility
An algebraic structure A is said to be finitely subdirectly reducible if A is not finitely subdirectly irreducible. We show that for any signature...
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Admissibility in Positive Logics
The paper studies admissibility of multiple-conclusion rules in positive logics. Using modification of a method employed by M. Wajsberg in the proof...
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A uniform Birkhoff theorem
Birkhoff’s HSP theorem characterizes the classes of models of algebraic theories as those being closed with respect to homomorphic images,...
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Canonical formulas for k-potent commutative, integral, residuated lattices
Canonical formulas are a powerful tool for studying intuitionistic and modal logics. Indeed, they provide a uniform and semantic way of axiomatising...
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Dualities and algebras with a near-unanimity term
Let P be a finite relational structure that admits a ( k + 1)-ary nearunanimity polymorphism. Then the NU Duality Theorem tells us that the algebra
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Joins of subalgebras and normals in 0-regular varieties
In any 0-normal variety (0-regular variety in which {0} is a subalgebra), every congruence class containing 0 is a subalgebra. These “normal...
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A juggler’s dozen of easy† problems
Is every dualizable finite algebra of finite signature finitely based? What is the likelihood that a random finite modular lattice directly...
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Testing for edge terms is decidable
This paper defines a computational problem, the edge-like problem, and proves that the problem is a decidable one when the input sets are finite. The...
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An algebraic hardness criterion for surjective constraint satisfaction
The constraint satisfaction problem (CSP) on a relational structure B is to decide, given a set of constraints on variables where the relations come...
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The class of completely representable polyadic algebras of infinite dimensions is elementary
Answering a question posed by Hodkinson, we show that for infinite ordinals α , every atomic polyadic algebra of dimension α (
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On inverse limits of monounary algebras
We study inverse limits of monounary algebras. All monounary algebras A such that A can arise from A only by an inverse limit construction are...
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Dualizing clones into categories of topological spaces
In this paper, we study clones of dual operations in the category of topological spaces. Our investigation is motivated by the possibility to apply...