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A Logiweb dictionary is an array that maps cardinals to cardinals.
Now consider a page whose reference cardinal is r. If the dictionary of the page maps the cardinal i to the cardinal a, then we say that the general symbol (r,i) is 'proper' and has 'arity' a.
Dictionaries are understood to map zero to zero. Hence, for any page r, the general symbol (r,0) is proper and has arity zero. We shall refer to (r,0) as the 'page symbol' of page r.
We shall say that a general symbol (r,i) is 'improper' in the following two cases. Case 1: no page on Logiweb has reference cardinal r. Case 2: Logiweb contains a page with reference cardinal r, but the dictionary of that page does not map i to anything.
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