A model-theoretic characterization of the weak pigeonhole principle Original Research Article

We bring together some facts about the weak pigeonhole principle (WPHP) from bounded arithmetic, complexity theory, cryptography and abstract model theory. We characterize the models of arithmetic in which WPHP fails as those which are determined by an initial segment and prove a conditional separation result in bounded arithmetic, that PV + (sharply bounded collection for PV formulas) lies strictly between PV and S21 in strength, assuming that the cryptosystem RSA is secure.