An independence of the MIN principle from the PHP principle

Mykyta Narusevych

An independence of the MIN principle from the PHP principle

Logic 2026-05-18 v5 Logic in Computer Science

Authors: Mykyta Narusevych

Abstract

The minimization principle $\textsf{MIN}(\triangleleft)$ studied in bounded arithmetic says that a strict linear ordering $\triangleleft$ on any finite interval $[0,\dots,n)$ has the minimal element. We shall prove that bounded arithmetic theory $\textsf{T}^1_2(\triangleleft)$ augmented by instances of the pigeonhole principle for all $\Delta^b_1(\triangleleft)$ formulas does not prove $\textsf{MIN}(\triangleleft)$ .

Keywords

bounded arithmetic minimization principle pigeonhole principle linear ordering finite interval

Cite

@article{arxiv.2406.14930,
  title  = {An independence of the MIN principle from the PHP principle},
  author = {Mykyta Narusevych},
  journal= {arXiv preprint arXiv:2406.14930},
  year   = {2026}
}

An independence of the MIN principle from the PHP principle

Abstract

Keywords

Cite

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