Model theory of bounded arithmetic with applications to independence results

In this paper we apply some new and some old methods in order to construct classical and intuitionistic models for theories of bounded arithmetic. We use these models to obtain proof theoretic consequences. In particular, we construct an ωchain of models of BASIC such that the union of its worlds satisfies S2 but none of its worlds satisfies the sentence ∀x∃y(x = 0 ∨ x = y + 1). Interpreting this chain as a Kripke model shows that double negation of the above mentioned sentence is not provable in the intuitionistic theory of BASIC plus polynomial induction on coNP formulas. 2000 Mathematics Subject Classification: 03F30, 03F55, 03F50, 68Q15.