The Super Amalgamation Property via Neat Embeddings, and a Problem of Henkin and Monk
نویسندگان
چکیده
We give a sufficient condition for a class of representable cylindric algebras to have the super amalgamation property. We show that the class of representable algebras (RCAα) does not satisfy this condition when α > 1, but if we restrict ourselves to the class of dimension complemented algebras (Dcα) then this condition is satisfied when α ≥ ω. Hence Dcα’s super amalgamate with respect to RCAα for α ≥ ω. An open problem of Henkin and Monk is solved. Mathematics Subject Classification: Primary 03G15. Secondary 03C05, 03C40
منابع مشابه
The Amalgamation Property and a Problem of Henkin, Monk and Tarski
Using the fact that the class of representable cylindric algebras of infinite dimension fails to have the amalgamation property, we solve an open problem in the monograph “Cylindric Algebras, Part I” by Henkin, Monk and Tarski. Our result applies to other algebras of logic, namely Pinter’s substitution algebras and Halmo’s quasi-polyadic algebras.
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