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See detailIntersections with Slupecki Partial Clones on a Finite Set
Schölzel, Karsten UL; Haddad, Lucien

in Multiple-Valued Logic (ISMVL), 2013 IEEE 43rd International Symposium on (2013, May)

We study intersections of partial clones on the k-element set with k ≥ 2. More precisely we consider intersections of Slupecki partial clones with non-Slupecki maximal partial clones on k.

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See detailA Solution to a Problem of D. Lau: Complete Classification of Intervals in the Lattice of Partial Boolean Clones
Schölzel, Karsten UL; Couceiro, Miguel UL; Haddad, Lucien et al

in Multiple-Valued Logic (ISMVL), 2013 IEEE 43rd International Symposium on (2013)

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 ... [more ▼]

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. [less ▲]

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