On the Amalgamation Base of Cylindric Algebras
نویسندگان
چکیده
Let K be a class of algebras. A0 ∈ K is in the amalgamation base of K, briefly A0 ∈ APbase(K), if for all A1,A2 ∈ K and monomorphisms i1 : A0 → A1 i2 : A0 → A2 there exist D ∈ K and monomorphisms m1 : A1 → D and m2 : A2 → D such that m1 ◦ i1 = m2 ◦ i2. CAα stands for the class of cylindric algebras of dimension α. We determine the amalgamation base for the class of representable CAα’s (RCAα). We also give a sufficient condition for A ∈ RCAα to belong to the super amalgamation base of RCAα, (SUPAPbase(RCAα)), exhibiting a concrete class that lies in this base when α ≥ ω. Finally, we show that SUPAPbase(RCAω) APbase(CAω) ∩ RCAω. In particular, APbaseRCAω = APbaseCAω∩RCAω. In the process, questions posed by Tarski, Monk and Pigozzi are answered. Mathematics Subject Classification: Primary 03G15. Secondary 03C05, 03C40
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