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Lattices of Algebraic Subsets and Implicational Classes

In: Lattice Theory: Special Topics and Applications

Author

Listed:
  • K. Adaricheva

    (Nazarbayev University, School of Science and Technology)

  • J. B. Nation

    (University of Hawaii, Department of Mathematics)

Abstract

In this section we consider one of the central constructions producing joinsemidistributive lattices, which turned out to be crucial in connecting many aspects of these lattices. The goal of this section is to present Sp(PowX), the lattice of algebraic subsets of the powerset lattice of some set X. We will need several definitions and lemmas on the way.

Suggested Citation

  • K. Adaricheva & J. B. Nation, 2016. "Lattices of Algebraic Subsets and Implicational Classes," Springer Books, in: George Grätzer & Friedrich Wehrung (ed.), Lattice Theory: Special Topics and Applications, chapter 0, pages 103-151, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-44236-5_4
    DOI: 10.1007/978-3-319-44236-5_4
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