Summary We show that Grothendieck's functor K o maps 3-subhomogeneous AF C * -algebras with Hausdorff structure space one-one onto countable Lindenbaum algebras of 3-valued logic. Whereas in the interpretation of Birkhoff and von Neumann propositions arc identified with projections and form an uncountable nondistributive lattice, in our interpretation propositions are unitary equivalence classes of projections, and form a countable MV 3 algebra of Chang and Grigolia, alias a 3-valued Lukasiewicz algebra in the sense of Moisil and Monteiro, that is, a Kleene algebra equipped with an operation ∇ obeying x * ∧ ∇ x = x * ∧ x and x * ∧ ∇ x = 1.