Geodesic
Connecting real and hyperarithmetical analysis
Documenta mathematica, Tome 29 (2024) no. 6, pp. 1469-1498

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Going back to Kreisel in the sixties, hyperarithmetical analysis is a cluster of logical systems just beyond arithmetical comprehension. Only recently natural examples of theorems from the mathematical mainstream were identified that fit this category. In this paper, we provide many examples of theorems of real analysis that sit within the range of hyperarithmetical analysis, namely between the higher-order version of Σ11​-AC0​ and weak-Σ11​-AC0​, working in Kohlenbach’s higher-order framework. Our example theorems are based on the Jordan decomposition theorem, unordered sums, metric spaces, and semi-continuous functions. Along the way, we identify a couple of new systems of hyperarithmetical analysis.
DOI : 10.4171/dm/981
Classification : 03F35, 03B30
Mots-clés : higher-order arithmetic, hyperarithmetical analysis 
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Sam Sanders. Connecting real and hyperarithmetical analysis. Documenta mathematica, Tome 29 (2024) no. 6, pp. 1469-1498. doi: 10.4171/dm/981

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