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arXiv · 2503.06758

Strongly increasing sequences

Paul B. Larson·Chris Lambie-Hanson
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Abstract

Using a variation of Woodin's $\mathbb{P}_{\mathrm{max}}$ forcing, we force over a model of the Axiom of Determinacy to produce a model of ZFC containing a very strongly increasing sequence of length $\omega_{2}$ consisting of functions from $\omega$ to $\omega$. We also show that there can be no such sequence of length $\omega_{4}$.

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Paul B. Larson, Chris Lambie-Hanson. 2025-03-09. Strongly increasing sequences. https://doi.org/10.1017/jsl.2026.10200

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