The computational content of Nonstandard Analysis

Sam Sanders
(LMU Munich and Ghent University)

Kohlenbach's proof mining program deals with the extraction of effective information from typically ineffective proofs. Proof mining has its roots in Kreisel's pioneering work on the so-called unwinding of proofs. The proof mining of classical mathematics is rather restricted in scope due to the existence of sentences without computational content which are provable from the law of excluded middle and which involve only two quantifier alternations. By contrast, we show that the proof mining of classical Nonstandard Analysis has a very large scope. In particular, we will observe that this scope includes any theorem of pure Nonstandard Analysis, where `pure' means that only nonstandard definitions (and not the epsilon-delta kind) are used. In this note, we survey results in analysis, computability theory, and Reverse Mathematics.

In Ulrich Kohlenbach, Steffen van Bakel and Stefano Berardi: Proceedings Sixth International Workshop on Classical Logic and Computation (CL&C 2016), Porto, Portugal , 23th June 2016, Electronic Proceedings in Theoretical Computer Science 213, pp. 24–40.
Published: 19th June 2016.

ArXived at: http://dx.doi.org/10.4204/EPTCS.213.3 bibtex PDF

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