a1 Institute of Computer Science, Academy of Sciences of the Czech Republic, Pod Vodarenskou Vezi 2, 182 07 Prague 8, Czech Republic, E-mail: [email protected]
a2 Department of Mathematics, University of Manchester, Manchester M139PL, U.K., E-mail: [email protected]
a3 Department of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW, U.K., E-mail: [email protected]
Can one extend crisp Peano arithmetic PA by a possibly many-valued predicate Tr(x) saying “x is true” and satisfying the “dequotation schema” for all sentences φ? This problem is investigated in the frame of Łukasiewicz infinitely valued logic.
(Received August 01 1997)
(Revised August 02 1998)