Deductive interpolation in Lukasiewicz logic and amalgamation of MV-algebras..
Daniele Mundici
Dept. of Mathematics "Ulisse Dini", University of Florence
Viale Morgagni 67/a, 50134 Florence, Italy
ABSTRACT
There are several prooofs of deductive interpolation
for Lukasiewicz infinite-valued propositional
logic, and amalgamation for MV-algebras. Some of them use the
categorical equivalence between MV-algebras and
unital l-groups (and then rely on Pierce's amalgamation
theorem), others use Panti's classification of
prime ideals in MV-algebras, others, like the
proof by Kihara and Ono, follow by applying to MV-algebras
general results in universal algebra. A short,
quite elementary proof can be given using the basic
properties of rational polyhedra, i.e., finite unions
of simplexes with rational vertices, and noting that
the zeroset of every McNaughton function f is a rational
polyhedron, and rational polyhedra are preserved under
projections onto rational hyperplanes.