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arXiv · 2609.00884

The weakness of typicality

Eric P. Astor·Laurent Bienvenu·Damir Dzhafarov·Ludovic Patey·Paul Shafer·Reed Solomon·Linda Westrick
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Abstract

Many statements studied in reverse mathematics can be seen as mathematical problems, formulated in terms of instances and solutions. We develop a framework of typicality encompassing measure and genericity, and we classify the reverse mathematics zoo in terms of which problems admit typical solutions. It turns out that even very weak problems do not admit typical solutions.

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Eric P. Astor, Laurent Bienvenu, Damir Dzhafarov, Ludovic Patey, Paul Shafer, Reed Solomon, Linda Westrick. 2026-09-01. The weakness of typicality. https://arxiv.org/abs/2609.00884

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