[Proof Complexity] Update to preprint

[Mykyta Narusevych]

Dear colleagues,

My preprint, "An independence of the MIN principle from the PHP principle," has been significantly changed and is now available at https://arxiv.org/abs/2406.14930.

We extend the typical forcing of M. Müller 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 $\forall T^1_2(PV(\alpha))$ augmented by the polynomial-time injective pigeonhole principle does not prove the linear ordering, tournament and dual weak pigeonhole principles.

Any comments or corrections are highly appreciated.

With regards

Mykyta Narusevych