Article

algebra universalis

, Volume 20, Issue 3, pp 328-350

The Birkhoff Variety Theorem for continuous algebras

  • Jiři AdámekAffiliated withFEL-CVUTMcMaster UniversityKatedra Matematiky, FJFI
  • , Evelyn NelsonAffiliated withFEL-CVUTMcMaster UniversityKatedra Matematiky, FJFI
  • , Jan ReitermanAffiliated withFEL-CVUTMcMaster UniversityKatedra Matematiky, FJFI

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Abstract

Varieties of continuous algebras, i.e., classes presented by (in)equalities for terms, are characterized as precisely the HSP classes. Terms here are the usual algebraic terms enriched by iterated join symbols. A discussion of varieties which require only finitely many variables, or only the usual terms, is also presented.