Dichotomy on intervals of strong partial Boolean clones
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- 作者：Karsten Sch?lzel
- 关键词：Primary ; 08A55 ; Secondary ; 03B50 ; partial clones ; Boolean clones ; intervals
- 刊名：Algebra Universalis
- 出版年：2015
- 出版时间：June 2015
- 年：2015
- 卷：73
- 期：3-4
- 页码：347-368
- 全文大小：762 KB
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1. University of Luxembourg, Mathematics Research Unit, 6, rue Richard Coudenhove-Kalergi, L-1359, Luxembourg, Grand Duchy of Luxembourg - 刊物类别：Mathematics and Statistics
- 刊物主题：Mathematics
Algebra - 出版者：Birkh盲user Basel
- ISSN：1420-8911
文摘
The following result has been shown recently in the form of a dichotomy: For every total clone C on := {0, 1}, the set \({\mathcal{I}}\)(C) of all partial clones on 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 , the set \({\mathcal{I}_{\rm Str}}\)(C) of all strong partial clones on whose total component is C, is either finite or of continuum cardinality.