According to the incompleteness theorems, a powerful-enough consistent axiomatic theory is incomplete, meaning the truth of some of its propositions cannot be established within its formalism. The statement above says that this incompleteness must include the solvability of a diophantine equation, assuming that the theory in question is a number theory.
According to the incompleteness theorems, a powerful-enough consisten.t axiomatic theory is incomplete, meaning the truth of some of its propositions cannot be established within its formalism The statement above says that this incompleten,ess must include the solvability of a diophantine equation assuming that the theory in question is a .number theory