Algebraic functions in Lukasiewicz implication algebras

CAMPERCHOLI, MIGUEL; CASTAÑO, DIEGO; DIAZ VARELA, PATRCIO

INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION

WORLD SCIENTIFIC PUBL CO PTE LTD

Lugar: London, UK; Año: 2016 vol. 26 p. 223 - 247

0218-1967

A function is algebraic on an algebra A if it is definable by a conjunction of equations on A. We fully characterize algebraic functions on every Lukasiewicz implication algebra belonging to a finitely generated variety. The main tool to accomplish this is a factorization result describing algebraic functions in a subproduct in terms of the algebraic functions of the factors. We prove a global representation theorem for finite Lukasiewicz implication algebras which extends a similar one already known for Tarski algebras. This result together with the knowledge of algebraic functions allowed us to give a partial description of the lattice of classes axiomatized by sentences of the form (A)(E)!&p=q within the variety generated by the 3-element chain.