Work

The weakness of typicality

Year: 2026

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.00884

Authors: Astor, Eric P., Bienvenu, Laurent, Dzhafarov, Damir, Patey, Ludovic, Shafer, Paul, Solomon, Reed, Westrick, Linda

Topic: Computability, Logic, AI Algorithms

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7206199949

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