A Note on Atom Structures of Relation and Cylindric Algebras
نویسندگان
چکیده
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 algebra with a dense representable subalgebra 4. RRA is not Sahlqvit axiomatizable. 5. There exists an atomic relation algebra with no complete representation. And same for RCAn for 2 < n < ω, in place of RA. Our proof substantially simplifies the proof of Hodkinson in [4]. Mathematics Subject Classification: Primary 03G15
منابع مشابه
Atom Structures of Cylindric Algebras and Relation Algebras
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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