Algebraic lattices are complete sublattices of the clone lattice over an infinite set

Michael Pinsker

Michael Pinsker

Fundamenta Mathematicae, Tome 193 (2007), p. 1-10 / Harvested from The Polish Digital Mathematics Library

Résumé

The clone lattice Cl(X) over an infinite set X is a complete algebraic lattice with $2^{| X |}$ compact elements. We show that every algebraic lattice with at most $2^{| X |}$ compact elements is a complete sublattice of Cl(X).

Publié le : 2007-01-01

Zbl 1127.08001

EUDML-ID : urn:eudml:doc:283363

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     author = {Michael Pinsker},
     title = {Algebraic lattices are complete sublattices of the clone lattice over an infinite set},
     journal = {Fundamenta Mathematicae},
     volume = {193},
     year = {2007},
     pages = {1-10},
     zbl = {1127.08001},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm195-1-1}
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Michael Pinsker. Algebraic lattices are complete sublattices of the clone lattice over an infinite set. Fundamenta Mathematicae, Tome 193 (2007) pp. 1-10. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm195-1-1/