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On the lower part of the lattice of partial clones

Miguel Couceiro 1 Lucien Haddad 2 Karsten Schölzel 3
1 ORPAILLEUR - Knowledge representation, reasonning
Inria Nancy - Grand Est, LORIA - NLPKD - Department of Natural Language Processing & Knowledge Discovery
Abstract : 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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Submitted on : Wednesday, October 31, 2018 - 9:00:59 AM
Last modification on : Wednesday, November 3, 2021 - 7:09:11 AM
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  • HAL Id : hal-01826870, version 4



Miguel Couceiro, Lucien Haddad, Karsten Schölzel. On the lower part of the lattice of partial clones. Journal of Multiple-Valued Logic and Soft Computing, Old City Publishing, In press. ⟨hal-01826870v4⟩



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