کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
6799279 | 542395 | 2016 | 14 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Universal semiorders
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات کاربردی
چکیده انگلیسی
A Z-product is a modified lexicographic product of three total preorders such that the middle factor is the chain of integers equipped with a shift operator. A Z-line is a Z-product having two linear orders as its extreme factors. We show that an arbitrary semiorder embeds into a Z-product having the transitive closure as its first factor, and a sliced trace as its last factor. Sliced traces are modified forms of traces induced by suitable integer-valued maps, and their definition is reminiscent of constructions related to the Scott-Suppes representation of a semiorder. Further, we show that Z-lines are universal semiorders, in the sense that they are semiorders, and each semiorder embeds into a Z-line. As a corollary of this description, we derive the well known fact that the dimension of a strict semiorder is at most three.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Mathematical Psychology - Volume 73, August 2016, Pages 80-93
Journal: Journal of Mathematical Psychology - Volume 73, August 2016, Pages 80-93
نویسندگان
Alfio Giarlotta, Stephen Watson,