Interpreting Lukasiewicz logic into Intuitionistic logic.
Vincenzo Marra, Daniel McNeill, Andrea Pedrini · 2014
The set of maximally consistent theories in L carries a natural topology that makes it homeomorphic to [0, 1]. The lattice Lfa is anti-isomorphic to the lattice of (cylindrified) rational polyhedra in [0, 1]. This is proved by passing to Lindenbaum-Tarski algebras, and applying the geometric duality theory of Chang’s MV-algebras, the algebraic counterparts of L. Algebraically, the lemma asserts the remarkable fact that the lattice of principal ideals of FL, the free MV-algebra on ω generators, is a countable Heyting algebra. This result is part of a more general investigation of the topology of prime spectral spaces of MV-algebras and related structures; see Andrea Pedrini’s submitted abstract. It follows that there is an onto homomorphism of Heyting algebras q : FInt Lfa,