Fragments of arithmetic and cyclic proofs

(jww with Daniyar Shamkanov and Ivan Smirnov)
We present an alternative cyclic proof system for Peano arithmetic that could be simpler than the existing ones and well-adapted both for proof analysis and for automatizing inductive proof search. In addition, we show how various traditional subsystems of Peano arithmetic defined by restricted forms of induction can be represented as fragments of the proposed system.