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algebra universalis

, Volume 54, Issue 1, pp 1–22 | Cite as

Full does not imply strong, does it?

  • Brian A. DaveyEmail author
  • Miroslav Haviar
  • Ross Willard
Original Paper

Abstract.

We give a duality for the variety of bounded distributive lattices that is not full (and therefore not strong) although it is full but not strong at the finite level. While this does not give a complete solution to the “Full vs Strong” Problem, which dates back to the beginnings of natural duality theory in 1980, it does solve it at the finite level. One consequence of this result is that although there is a Duality Compactness Theorem, which says that if an alter ego of finite type yields a duality at the finite level then it yields a duality, there cannot be a corresponding Full Duality Compactness Theorem.

Mathematics Subject Classification (2000).

06D50 08C05 08C15 18A40 08A55 

Keywords and phrases.

Natural duality full duality strong duality distributive lattices 

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Copyright information

© Birkhäuser Verlag, Basel 2005

Authors and Affiliations

  • Brian A. Davey
    • 1
    Email author
  • Miroslav Haviar
    • 2
  • Ross Willard
    • 3
  1. 1.Department of MathematicsLa Trobe University Australia
  2. 2.Department of MathematicsMatej Bel UniversityBanska BystricaSlovak Republic
  3. 3.Department of Pure MathematicsUniversity of WaterlooWaterlooCanada

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