Paper Info

Title | ||
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Intersections of isotone clones on a finite set |

Abstract | ||
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Let ⩽ be a fixed order of height at least 2 on a set A (i.e. contains a chain a<b<c). It is shown that all the isotone clones preserving orders on A isomorphic to ⩽ intersect in the clone KA of trivial functions (i.e. all the projections and all the constant operations on A). It is further shown that for A finite with at least eight elements and for any six-element set there exist two orders on A such that every joint endomorphism is trivial (i.e. idA or constants). The same is true for intersections of isotone clones. This yields that with the above restrictions there are four maximal isotone clones intersecting in KA. Separate considerations are given on the intersections of maximal isotone clones for |A|=3 and 4 |

Year | DOI | Venue |
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1990 | 10.1109/ISMVL.1990.122629 | Charlotte, NC |

Keywords | Field | DocType |

many-valued logics,set theory,endomorphism,finite set,fixed order,intersections,isotone clones,trivial functions | Discrete mathematics,Set theory,Combinatorics,Finite set,Lattice (order),Isomorphism,Isotone,Mathematics,Endomorphism | Conference |

Citations | PageRank | References |

10 | 2.99 | 1 |

Authors | ||

5 |

Authors (5 rows)

Cited by (10 rows)

References (1 rows)

Name | Order | Citations | PageRank |
---|---|---|---|

János Demetrovics | 1 | 414 | 163.60 |

Masahiro Miyakawa | 2 | 109 | 39.01 |

Ivo G. Rosenberg | 3 | 144 | 48.86 |

Dan A. Simovici | 4 | 410 | 67.83 |

Ivan Stojmenovic | 5 | 6553 | 520.25 |