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Tarek Sayed Ahmed

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On amalgamation of reducts of polyadic algebras

Following research initiated by Tarski, Craig and Németi, and further
pursued by Sain, we show that for certain subsets G of mappings from omega
to omega, G-polyadic-algebras have the strong amalgamation property. Here
omega denotes the set of natural numbers, and G-polyadic-algebras are obtained
by restricting (the similarity type) and axiomatization of omega-dimensional
polyadic algebras to finite quantifiers and substitutions in G. Using
algebraic logic, we infer that for certain proper extensions of first order
logic without equality, the theorems of Beth, Craig and Robinson hold.

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