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From: Mamuka Jibladze <jib@rmi.acnet.ge>
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Subject: Re: David Benson's questions on terminology
Date: Wed, 29 Nov 2000 15:12:53 +0200 (EET)
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> 	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