Abstract
Following research initiated by Tarski, Craig and Nemeti, and further pursued by Sain and others, we show that for certain subsets G of ωw, G polyadic algebras have the strong amalgamation property. G polyadic algebras are obtained by restricting the (similarity type and) axiomatization of ω-dimensional polyadic algebras to finite quantifiers and substitutions in G. Using algebraic logic, we infer that some theorems of Beth, Craig and Robinson hold for certain proper extensions of first order logic (without equality).
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