Representable semilattice-ordered monoids
Robin Hirsch,Szabolcs Mikulás +1 more
TL;DR: In this article, it was shown that no finite set of first-order axioms can define the class of representable semilattice-ordered monoids, and hence no class of monoid classes can be represented by first order axiomatizations.
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Abstract: We show that no finite set of first-order axioms can define the class of representable semilattice-ordered monoids.
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Citations
Axiomatizability of positive algebras of binary relations
Hajnal Andréka,Szabolcs Mikulás +1 more
TL;DR: In this article, the authors consider all positive fragments of Tarski's representable relation algebras and determine whether the equational and quasiequational theories of these fragments are finitely axiomatizable in first order logic.
Undecidability of representability as binary relations
Robin Hirsch,Marcel Jackson +1 more
TL;DR: This article establishes the undecidability of representability and of finite representability as algebras of binary relations in a wide range of signatures and establishes that representability is undecidable for Boolean monoids and lattice ordered monoids, while representability has been established for Jónsson's relation algebra.
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Axiomatizability of representable domain algebras
Robin Hirsch,Szabolcs Mikulás +1 more
TL;DR: It is proved that, even for the minimal signature consisting of the domain and composition operations, the class of representable domain algebras is not finitely axiomatizable.
18
Positive fragments of relevance logic and algebras of binary relations
Robin Hirsch,Szabolcs Mikulás +1 more
TL;DR: It is proved that algebras of binary relations whose similarity type includes intersection, union, and one of the residuals of relation composition form a nonfinitely axiomatizable quasivariety and that the equational theory is not finitely based.
Lower Semilattice-Ordered Residuated Semigroups and Substructural Logics
TL;DR: This work looks at lower semilattice-ordered residuated semigroups and, in particular, the representable ones, i.e., those that are isomorphic to algebras of binary relations, and gives finite axiomatizations for several notions of validity.
References
On the Calculus of Relations
TL;DR: The logical theory which is called the calculus of (binary) relations, and which will constitute the subject of this paper, has had a strange and rather capricious line of historical development.
Representations of distributive lattice-ordered semigroups with binary relations
TL;DR: In this paper, it was shown that R(∩, ∩, ¦) is not a variety and is not finitely axiomatizable, and moreover, if (A, ∨, ∧, ∘) ∈ DLOS then it is representable whenever we disregard one of its operations.
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