Kreisel's Conjecture with minimality principle
Pavel Hrubeš · Journal of Symbolic Logic · 2009
Abstract We prove that Kreisel's Conjecture is true, if Peano arithmetic is axiomatised using minimality principle and axioms of identity (theory PAM). The result is independent on the choice of language of PAM. We also show that if infinitely many instances of A(x) are provable in a bounded number of steps in PAM then there exists . The results imply that PAM does not prove scheme of induction or identity schemes in a bounded number of steps.