Preservation theorems and restricted consistency statements in bounded arithmetic
In the paper a new restricted consistency notion RCON\(^{\ast}(T^{j}_{2})\) for bounded arithmetic theories \(T^{j}_{2}\) is introduced and studied. It is the strongest \(\forall \Pi^{b}_{1}\)-statement over \(S^{1}_{2}\) provable in \(T^{j}_{2}\), similar to \(\text{Con}(G_{i})\) of Krajiček and Pudlák or \(\text{RCON}(T{i}_{1})\) of Krajiček and Takeuti. The advantage of the introduced new notion is that it can directly be used to construct models of \(T^{j}_{2}\). It is applied by proving preservation theorems for certain theories of bounded arithmetic.
scientific article; zbMATH DE number 2083182
scientific article