Reference : Dichotomy on intervals of strong partial Boolean clones
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/10993/9390
Dichotomy on intervals of strong partial Boolean clones
English
Schölzel, Karsten mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Jun-2015
Algebra Universalis
Springer Science & Business Media B.V.
73
3
347-368
Yes (verified by ORBilu)
0002-5240
[en] partial clones ; Boolean clones ; intervals
[en] The following result has been shown recently in the form of a dichotomy:
For every total clone $C$ on $\2 := \{0,1\}$, the set $\intervalD{C}$ of all partial clones on $\2$
whose total component is $C$, is either finite or of continuum cardinality. In this paper we show
that the dichotomy holds, even if only strong partial clones are considered, i.e., partial clones
which are closed under taking subfunctions:
For every total clone $C$ on $\2$, the set $\intervalStr{C}$ of all strong partial clones on $\2$
whose total component is $C$, is either finite or of continuum cardinality.
Researchers
http://hdl.handle.net/10993/9390
10.1007/s00012-015-0330-7
http://link.springer.com/article/10.1007/s00012-015-0330-7#/page-1

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