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arXiv · 1912.03487

Where Pigeonhole Principles meet König Lemmas

David Belanger·Chitat Chong·Wei Wang·Tin Lok Wong·Yue Yang
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Abstract

We study the pigeonhole principle for $Σ_2$-definable injections with domain twice as large as the codomain, and the weak König lemma for $Δ^0_2$-definable trees in which every level has at least half of the possible nodes. We show that the latter implies the existence of $2$-random reals, and is conservative over the former. We also show that the former is strictly weaker than the usual pigeonhole principle for $Σ_2$-definable injections.

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David Belanger, Chitat Chong, Wei Wang, Tin Lok Wong, Yue Yang. 2019-12-07. Where Pigeonhole Principles meet König Lemmas. https://arxiv.org/abs/1912.03487

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