Comparing Constructive Arithmetical Theories Based on NP-PIND and coNP-PIND
Mojtaba Moniri · Journal of Logic and Computation · 2003
In this note we show that the intuitionistic theory of polynomial induction on ∏1b+-formulas does not imply the intuitionistic theory I S21 of polynomial induction on ∑1b+-formulas. We also show the converse assuming the Polynomial Hierarchy does not collapse. Similar results hold also for length induction in place of polynomial induction. We also investigate the relation between various other intuitionistic first-order theories of bounded arithmetic. Our method is mostly semantical, we use Kripke models of the theories.