INDUCTIVE COMPLEXITY MEASURES FOR MATHEMATICAL PROBLEMS

An algorithmic uniform method to measure the complexity of statements of finitely refutable statements [6, 7, 8], was used to classify famous/interesting mathematical statements like Fermat's last theorem, Hilberts tenth problem, the four colour theorem, the Riemann hypothesis, [8, 15, 16]. Working with inductive Turing machines of various orders [1] instead of classical computations, we propose a class of inductive complexity classes for mathematical statements which generalise the previous method. In particular, the new method is capable to classify Pi(2)-statements. As illustrations, we evaluate the inductive complexity of the Collatz and twin prime conjecture - statements which cannot not be evaluated with the original method.