Strictly Order-Preserving Maps into Z, II. A 1979 Problem of Erné
نویسندگان
چکیده
Abstract. 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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ورودعنوان ژورنال:
- Order
دوره 18 شماره
صفحات -
تاریخ انتشار 2001