29 Nov
2000
29 Nov
'00
9:25 a.m.
Universal algebraists (but not category theorists??) call b the _cover_ of a when a<b with nothing in between. See e.g. the index of such lattice theory texts as Davey and Priestley or McKenzie, McNulty and Taylor (Walter). (MM&T distinguish upper cover and lower cover but obviously an unqualified cover has to mean the upper kind to all but us Aussies.) In a well-ordered set, "cover" and "successor" are synonymous: an ordinal is a cover just when it is a successor ordinal. Managed not to mention reflexivity---oops. Vaughan Pratt