We extend the typical forcing of M. M\"uller and derive conditions on the forcing frame for which generic expansions preserve injective/bijective pigeonhole principle for polynomial-time computable graphs of functions. Applying this machinery, we show that the bounded arithmetic theory $\forall \textsf{T}^1_2(\textsf{PV}(\alpha))$ augmented by the polynomial-time injective pigeonhole principle does not prove the linear ordering, tournament, and dual weak pigeonhole principles.

翻译：我们推广了M. M\"uller的典型力迫法，并推导出力迫框架的若干条件，使得在该框架下生成的泛型扩张能保持多项式时间可计算函数图的单射/双射鸽笼原理。应用这一工具，我们证明了由多项式时间单射鸽笼原理增强的有界算术理论$\forall \textsf{T}^1_2(\textsf{PV}(\alpha))$不能推导出线性序原理、锦标赛原理及对偶弱鸽笼原理。