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Journal Articles Journal of Multiple-Valued Logic and Soft Computing Year : 2019

On the lower part of the lattice of partial clones

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Miguel Couceiro
Lucien Haddad
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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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Dates and versions

hal-01826870 , version 1 (02-07-2018)
hal-01826870 , version 2 (24-07-2018)
hal-01826870 , version 3 (30-10-2018)
hal-01826870 , version 4 (31-10-2018)

Identifiers

  • HAL Id : hal-01826870 , version 4

Cite

Miguel Couceiro, Lucien Haddad, Karsten Schölzel. On the lower part of the lattice of partial clones. Journal of Multiple-Valued Logic and Soft Computing, 2019, 33 (3), pp.177-196. ⟨hal-01826870v4⟩
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