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On the Lower Part of the Lattice of Partial Clones
Miguel Couceiro, Lucien Haddad and Karsten Schölzel

Let k be a k-element set. We show that the lattice of all strong partial clones on k has no minimal elements. Moreover, we show that if C is a strong partial clone, then the family of all partial subclones of C is of continuum cardinality. Finally we show that every non-trivial strong partial clone contains a family of continuum cardinality of strong partial subclones.

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