Semirigid Systems of Three Equivalence Relations

被引：0

作者：

Delhomme, Christian ^{[1
]}

Miyakawa, Masahiro ^{[2
]}

Pouzet, Maurice ^{[3
,4
]}

Rosenberg, Ivo G. ^{[5
,6
]}

Tatsumi, Hisayuki ^{[2
]}

机构：

[1] Univ La Reunion, Dept Math & Informat, Lim Ermit, 15 Ave Rene Cassin,BP 7151, F-97715 St Denis Messag 9, France

[2] Tsukuba Univ Technol, 4-12-7 Kasuga, Tsukuba, Ibaraki 3058521, Japan

[3] Univ Claude Bernard Lyon1, UMR 5208, CNRS, Inst Camille Jordan, 43,Bd 11 Novembre 1918, F-69622 Villeurbanne, France

[4] Univ Calgary, Dept Math & Stat, Calgary, AB, Canada

[5] Univ Montreal, CP 6128,Succ Ctr Ville, Montreal, PQ H3C 3J7, Canada

[6] Masaryk Univ, Dept Math & Stat, Brno, Czech Republic

来源：

JOURNAL OF MULTIPLE-VALUED LOGIC AND SOFT COMPUTING | 2017年 / 28卷 / 4-5期

关键词：

Clones; rigidity; semirigidity; equivalence relations; 3-nets; latin squares; quasigroups; GENERALIZED ULTRAMETRIC SPACES;

D O I：

暂无

中图分类号：

TP18 [人工智能理论];

学科分类号：

081104 ; 0812 ; 0835 ; 1405 ;

摘要：

A system M of equivalence relations on a set E is semirigid if only the identity and constant functions preserve all members of M. We construct semirigid systems of three equivalence relations. Our construction leads to the examples given by Zadori in 1983 and to many others and also extends to some infinite cardinalities. As a consequence, we show that on every set of at most continuum cardinality distinct from 2 and 4 there exists a semirigid system of three equivalence relations.

引用

页码：511 / 535

页数：25

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