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. Müller的典型力迫法，并推导出力迫框架的条件，使得在该条件下一般扩张能保持多项式时间可计算函数图的注入/双射鸽巢原理。应用这一工具，我们证明了由多项式时间注入鸽巢原理增强的有界算术理论$\forall \textsf{T}^1_2(\textsf{PV}(\alpha))$不能证明线性序原理、锦标赛原理及对偶弱鸽巢原理。