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arXiv · 2603.20905

Combinatorial Properties Related to the Higher Baumgartner's Axiom

John Krueger
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Abstract

We isolate two combinatorial properties, each expressible by a $\Pi_2$-sentence over the structure $(H(\omega_3),\in,\omega_1,\omega_2,\text{NS}_{\omega_2})$, such that each property is consistent with CH, and their conjunction together with $2^\omega \le \omega_2$ and $2^{\omega_1} = 2^{\omega_2} = \omega_3$ implies the existence of a c.c.c. forcing which forces the higher Baumgartner's axiom.

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John Krueger. 2026-03-21. Combinatorial Properties Related to the Higher Baumgartner's Axiom. https://arxiv.org/abs/2603.20905

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