MODEL THEORY AND PROOF THEORY OF THE GLOBAL REFLECTION PRINCIPLE

Abstract The current paper studies the formal properties of Global Reflection Principle, to wit assertion “All theorems $\mathrm {Th}$ are true,” where is a theory in language arithmetic and truth predicate satisfies usual Tarskian inductive conditions for formulae arithmetic. We fix gap Kotlarski’s proof from [15], showing that Principle Peano Arithmetic provable compositional with bounded induction only ( {CT}_0$ ). Furthermore, we extend above result $\Sigma _1$ -uniform reflection over uniform Tarski biconditionals {UTB}^-$ ) , thus answering question Beklemishev Pakhomov [2]. Finally, introduce notion prolongable satisfaction class use it study structure models . In particular, provide new model-theoretical characterization theories finite iterations present characterizing arithmetical consequences