Algebraic functions

CAMPERCHOLI, MIGUEL; VAGGIONE, DIEGO

STUDIA LOGICA

Springer-Verlag

Año: 2011 vol. 98 p. 285 - 306

0039-3215

Let A be an algebra. We say that the functions f₁,...,f_{m}:Aⁿ→A are algebraic on A provided there is a finite system of term-equalities ⋀t_{k}(x,z)=s_{k}(x,z) satisfying that for each a∈Aⁿ, the m-tuple (f₁(a),...,f_{m}(a)) is the unique solution in A^{m} to the system ⋀t_{k}(a,z)=s_{k}(a,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.