J. Ulisses Ferreira, Federal University of Bahia, Brazil

This short and informal article shows that there exists some deductive system that proves that arithmetic is both sound and complete. First, it shows that there exists some four-valued logical system that plays the same role, by presenting a four-valued logic and informally introducing a four-valued Prolog programming language. Finally, it observes that some Boolean formal system can also prove that arithmetic is both sound and complete.

Gödel, incompleteness theorem, four-valued logic, logic, computability theory, philosophy of computer science