Strictly Order-Preserving Maps into Z, II. A 1979 Problem of Erné

被引：0
|
作者：
Jonathan David Farley
Bernd S. W. Schröder
机构：
[1] Vanderbilt University,Department of Mathematics
[2] Mathematical Sciences Research Institute,Program of Mathematics and Statistics
[3] Louisiana Tech University,Department of Mathematics
[4] Hampton University,undefined
来源：
Order | 2001年 / 18卷
关键词：
chain; lattice; (partially) ordered set; (strictly) order-preserving map;
D O I：
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学科分类号：
摘要：
A lattice L is constructed with the property that every interval has finite height, but there exists no strictly order-preserving map from L to Z. A 1979 problem of Erné (posed at the 1981 Banff Conference on Ordered Sets) is thus solved. It is also shown that if a poset P has no uncountable antichains, then it admits a strictly order-preserving map into Z if and only if every interval has finite height.
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页码：381 / 385
页数：4
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