algebra universalis

, Volume 20, Issue 3, pp 328–350 | Cite as

The Birkhoff Variety Theorem for continuous algebras

  • Jiři Adámek
  • Evelyn Nelson
  • Jan Reiterman


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.


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Copyright information

© Birkhäuser Verlag 1985

Authors and Affiliations

  • Jiři Adámek
    • 1
    • 2
    • 3
  • Evelyn Nelson
    • 1
    • 2
    • 3
  • Jan Reiterman
    • 1
    • 2
    • 3
  1. 1.FEL-CVUTPrahaCzechoslovakia
  2. 2.McMaster UniversityHamiltonCanada
  3. 3.Katedra MatematikyFJFIPrahaCzechoslovakia

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