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Conference Papers Year : 2017

On the nonexistence of minimal strong 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. We also show that in almost all cases, every strong partial clone contains a family of continuum cardinality of strong partial subclones.
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Dates and versions

hal-01504011 , version 1 (08-04-2017)

Identifiers

  • HAL Id : hal-01504011 , version 1

Cite

Miguel Couceiro, Lucien Haddad, Karsten Schölzel. On the nonexistence of minimal strong partial clones. ISMVL 2017 - 47th IEEE International Symposium on Multiple-Valued Logic, May 2017, Novi Sad, Serbia. pp.6. ⟨hal-01504011⟩
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