Strongly representable atom structures of relation algebras
نویسندگان
چکیده
منابع مشابه
Strongly Representable Atom Structures of Relation Algebras
A relation algebra atom structure α is said to be strongly representable if all atomic relation algebras with that atom structure are representable. This is equivalent to saying that the complex algebra Cmα is a representable relation algebra. We show that the class of all strongly representable relation algebra atom structures is not closed under ultraproducts and is therefore not elementary. ...
متن کاملStrongly representable atom structures of cylindric algebras
A cylindric algebra atom structure is said to be strongly representable if all atomic cylindric algebras with that atom structure are representable. This is equivalent to saying that the full complex algebra of the atom structure is a representable cylindric algebra. We show that for any finite n ≥ 3, the class of all strongly representable n-dimensional cylindric algebra atom structures is not...
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A boolean algebra is shown to be completely representable if and only if it is atomic whereas it is shown that the class of completely representable relation algebras is not elementary.
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For any finite n ≥ 3 there are two atomic n-dimensional cylindric algebras with the same atom structure, with one representable, the other, not. Hence, the complex algebra of the atom structure of a representable atomic cylindric algebra is not always representable, so that the class RCAn of representable n-dimensional cylindric algebras is not closed under completions. Further, it follows by a...
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RRA stands for the class of representable relation algebras, while RCAn stands for the class of cylindric algebras of dimension n. We give a simple new proof to the following. 1. There exist two atomic relation algebras with the same atom structure, only one of which is representable. 2. RRA is not closed under completions and is not atom-canonical. 3. There exists a non-representable relation ...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2001
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-01-06232-3