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*To*: categories@mta.ca*Subject*: categories: Re: David Benson's questions on terminology*From*: Mamuka Jibladze <jib@rmi.acnet.ge>*Date*: Wed, 29 Nov 2000 15:12:53 +0200 (EET)*In-Reply-To*: <3A24002A.2762B24B@stmarys.ca>*Reply-To*: Mamuka Jibladze <jib@rmi.acnet.ge>*Sender*: cat-dist@mta.ca

> I don't think David was trying to generalize the successor > relation in the sense of finding a "moral equivalent" in a poset for > the natural numbers' successor _function_. All he wants - I think - > is a notation for "a > b and there is no a>c>b". I would suggest > using an indefinite article with a noun formation: > > " a is _a_ successor of b" > > or a prepositional formation that does not connote uniqueness or > necessary existence: > > "a is immediately above b" > > Bob Pare and I used "<!" for this in our 1993 paper on tileorders. In that case I believe there is established terminology/notation in lattice theory, they say "a covers b", denoted b -< a, and corresponding intervals (i.e. intervals with [a,b]={a,b}) are called gaps. Mamuka

**References**:**categories: Re: David Benson's questions on terminology***From:*"Robert J. MacG. Dawson" <Robert.Dawson@STMARYS.CA>

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