Restricted polynomial induction versus ordinary induction
Tom 242 / 2018
Streszczenie
We consider conservativity questions between, on the one hand, arithmetical theories in which the operations of successor, addition and multiplication are not provably total and which are fragments of the bounded arithmetic theory and, on the other hand, extensions of those theories to subtheories of Buss’s bounded arithmetic S_2. These questions are related to the problem of finite axiomatizability of a version of I\Delta _0 in which the totality of the operations is not assumed.