Online research in philosophy

Let A be an algebra. We say that the functions f 1 , . . . , f m : A n → A are algebraic on A provided there is a finite system of term-equalities $${{\bigwedge t_{k}(\overline{x}, \overline{z}) = s_{k}(\overline{x}, \overline{z})}}$$ satisfying that for each $${{\overline{a} \in A^{n}}}$$, the m -tuple $${{(f_{1}(\overline{a}), \ldots , f_{m}(\overline{a}))}}$$ is the unique solution in A m to the system $${{\bigwedge t_{k}(\overline{a}, \overline{z}) = s_{k}(\overline{a}, \overline{z})}}$$. In this work we present a collection of general (...) tools for the study of algebraic functions, and apply them to obtain characterizations for algebraic functions on distributive lattices, Stone algebras, finite abelian groups and vector spaces, among other well known algebraic structures. (shrink)

In this paper we study some questions concerning Łukasiewicz implication algebras. In particular, we show that every subquasivariety of Łukasiewicz implication algebras is, in fact, a variety. We also derive some characterizations of congruence permutable algebras. The starting point for these results is a representation of finite Łukasiewicz implication algebras as upwardly-closed subsets in direct products of MV-chains.