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*To*: categories@mta.ca*Subject*: categories: More about names and notation*From*: "David B. Benson" <dbenson@eecs.wsu.edu>*Date*: Tue, 28 Nov 2000 12:51:18 -0800*Sender*: cat-dist@mta.ca

Dear Colleagues, Thank you for the responses! (1) Several pointed out that my <<followers>> relations are said to be <<covering>> relations in combinatorics. These relations are defined as relations which are 1. acyclic 2. without interpolants, as Robert Dawson mentioned. A followers relation for discrete partial order R is the least relation whose reflexive and transitive closure is R. This agrees entirely with the definition of a successor relation being the least relation whose transitive closure is a discrete strict total order and whose reflexive and transitive closure is a discrete total order. In the case of successor, there is a distinct next element, as in the succession of the Kings (and Queens) of England. In the case of followers, there is in general a set of next elements, such as the followers of Cromwell. (2) While several alternatives were offered, I will try Paul Taylor's <<instance>> of a relation to describe an ordered pair (x,y) \in R. (3) The problem of a good name for the sets Nat_k remains. Suggestions included finite ordinals numerals order ideals and by far the most appropriate for my purposes, index sets [This problem of a good name is worthy of some further attention. Computer science second year students will think of <<finite ordinals>> as a number, not a set, of <<numerals>> as representations of the digits in a number system, and have not be exposed to order ideals.] Cheers, David -- Professor David B. Benson (509) 335-2706 School of EE and Computer Science (EME 102A) (509) 335-3818 fax PO Box 642752, Washington State University dbenson@eecs.wsu.edu Pullman WA 99164-2752 U.S.A.

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