Year: 2024
Type: article
Abstract: 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 \Sigma_{1}^{1} - \mathsf{AC}_{0} and \mathsf{weak} - \Sigma_{1}^{1} - \mathsf{AC}_{0} , 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.
Source: Documenta Mathematica
DOI: 10.4171/dm/981
Author: Sam Sanders
Institution: Ruhr University Bochum
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4404721081