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The recent development of abstract algebraic logic has led to a reconsideration of the universal algebraic theory of ordered algebras from a new perspective. The familiar equational logic of Birkhoff can be naturally viewed as one of the deductive systems that constitute the main object of study in abstract algebraic logic; technically it is a deductive(More)
Lambda abstraction algebras (LAAs) are designed to algebraize the untyped lambda calculus in the same way cylindric and polyadic algebras algebraize the first-order predicate logic. Like combinatory algebras they can be defined by true identities and thus form a variety in the sense of universal algebra, but they differ from combinatory algebras in several(More)
An infinite sequence ∆ = ∆n(x0,. .. , xn−1, y, ¯ u) : n < ω of possibly infinite sets of formulas in n + 1 variables x0,. .. , xn−1, y and a possibly infinite system of parameters ¯ u is a parameterized graded deduction-detachment (PGDD) system for a de-ductive system S over a S-theory T if, for every n < ω and for all ϕ0,. ϑ) for every possible system of(More)