General algebraic systems Clones and operations Concept
Lattice of clones
Summary
The lattice of clones on a set is the set of all clones on , ordered by inclusion. It is a complete lattice: the meet of a family of clones is its intersection, and the join is the clone generated by the union. Its least element is the clone of projections and its greatest element is the clone of all finitary operations. On a two-element set it is countable, and Post's lattice describes it completely. On a finite set with at least three elements it has the cardinality of the continuum.
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| Tag | EX9NCDFYC7 |
|---|---|
| URI | m2://EX9NCDFYC7 |
| Kind | concept |
| Writing | W0 stub |
| MSC | 08A40, 06B23 |
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