Algebraic functions in Lukasiewicz implication algebras

DÍAZ VARELA JOSÉ PATRICIO; CASTAÑO DIEGO; CAMPERCHOLI MIGUEL

INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION

WORLD SCIENTIFIC PUBL CO PTE LTD

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

0218-1967

In this article we study algebraic functions in {→,1}{→,1}-subreducts of MV-algebras, also known as Łukasiewicz implication algebras. A function is algebraic on an algebra AA if it is definable by a conjunction of equations on AA. We fully characterize algebraic functions on every Łukasiewicz 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 Łukasiewicz 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 ∀∃!∧p≈q∀∃!∧p≈q within the variety generated by the 3-element chain.Read More: http://www.worldscientific.com/doi/10.1142/S0218196716500119