Representable semilattice-ordered monoids

Hirsch, Robin; Mikulás, Szabolcs

doi:10.1007/s00012-007-2055-8

Cited by 14 publications

(7 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The class R( · , ; , 1 ) is not finitely axiomatizable, [15]. The same holds if we include 0 and/or a top element 1 (whose representation is a reflexive and transitive relation).…”

Section: Quasivarietiesmentioning

confidence: 89%

Axiomatizability of positive algebras of binary relations

Andréka

Mikulás

2011

Algebra Univers.

Self Cite

View full text Add to dashboard Cite

show abstract

“…The class R( · , ; , 1 ) is not finitely axiomatizable, [15]. The same holds if we include 0 and/or a top element 1 (whose representation is a reflexive and transitive relation).…”

Section: Quasivarietiesmentioning

confidence: 89%

Axiomatizability of positive algebras of binary relations

Andréka

Mikulás

2011

Algebra Univers.

Self Cite

View full text Add to dashboard Cite

show abstract

“…Andréka [An91] shows non-finite axiomatizability for representable algebras of similarity type τ ⊇ {• , +, ;}. In [HM07], we defined non-representable algebras of the similarity type {• , 1 , ;} whose ultraproduct is representable. Since 1 is a minimal non-zero element in these algebras, defining domain, range and antidomain operations should not be a problem.…”

Section: Any Non-trivial Ultraproductmentioning

confidence: 99%

Axiomatizability of representable domain algebras

Hirsch

Mikulás

2011

The Journal of Logic and Algebraic Programming

Self Cite

View full text Add to dashboard Cite

The family of domain algebras provide an elegant formal system for automated reasoning about programme verification. Their primary models are algebras of relations, viz. representable domain algebras. We prove that, even for the minimal signature consisting of the domain and composition operations, the class of representable domain algebras is not finitely axiomatizable. Then we show similar results for extended similarity types of domain algebras.

show abstract

“…The subreduct that we focus on in this work is RRA(•, ∩, 1), the restriction of RRA to the operations of composition, intersection and the identity relation, also known as the class of representable semi-lattice ordered monoids. It was deeply studied in [2] and [8]. For example, its equational theory is decidable [1] but not finitely axiomatizable [5].…”

Section: Introductionmentioning

confidence: 99%