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A Solution to a Problem of D. Lau: Complete Classification of Intervals in the Lattice of Partial Boolean Clones
Miguel Couceiro, Lucien Haddad, Karsten Schölzel and Tamás Waldhauser

The following natural problem, first considered by D. Lau, has been tackled by several authors recently: Let C be a total clone on 2 := {0, 1}. Describe the interval I(C) of all partial clones on 2 whose total component is C. We establish some results in this direction and combine them with previous ones to show the following dichotomy result: For every total clone C on 2, the set I(C) is either finite or of continuum cardinality.

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