Amalgamation of polyadic algebras

On Amalgamation of Reducts of Polyadic Algebras

Reducts of Polyadic Equality Algebras without the Amalgamation Property

Let G ⊆ ω be a monoid such that {[i|j ] : i, j ∈ ω} ⊆ G. Let RPEAG be the reduct of representable polyadic equality algebras obtained by restricting the similarity type of RPEAω to substitutions in G and PEAG be the class of abstract polyadic algebras obtained from PEAω by restricting the similarity type and axiomatization of PEAω to substitutions in G and to finite quantifiers. Assume that G c...

Amalgamation for Reducts of Polyadic Equality Algebras, a Negative Result

Let G ⊆ ω be a semigroup. G polyadic algebras with equality, or simply G algebras, are reducts of polyadic algebras with equality obtained by restricting the similarity type and axiomatization of polyadic algebras to substitutions in G, and possibly weakening the axioms governing diagonal elements. Such algebras were introduced in the context of ’finitizing’ first order logic with equality. We ...

Amalgamation for Reducts of Polyadic Equality Algebras, both a Negative Result and a Positive Result

Let G ⊆ ωω be a semigroup. G polyadic algebras with equality, or simply G algebras, are reducts of polyadic algebras with equality obtained by restricting the similarity type and axiomatization of polyadic algebras to substitutions in G, and possibly weakening the axioms governing the diagonal elements. Such algebras were introduced in the context of ’finitizing’ first order logic with equality...

An autobiography of Polyadic Algebras

In the 1950’s I set out to revolutionize logic. I didn’t succeed (not yet!), but it wasn’t for want of trying. Logic has always fascinated me. In the common-sense sense of the word logic was easy; I had no inclination to commit the obvious errors of reasoning, and long chains of deductions were not intimidating. When I was told about syllogisms, I said “sure, obviously”, and didn’t feel that I ...