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Proof mining and combinatorics : Program extraction for Ramsey's theorem for pairs

Kreuzer, Alexander P. :
Proof mining and combinatorics : Program extraction for Ramsey's theorem for pairs.
TU Darmstadt
[Ph.D. Thesis], (2012)

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Item Type: Ph.D. Thesis
Title: Proof mining and combinatorics : Program extraction for Ramsey's theorem for pairs
Language: English
Abstract:

In this thesis we give a proof-theoretic account of the strength of Ramsey's theorem for pairs and related principles. We develop a method to extract programs from proofs using this theorem. Moreover, we consider the strength of different variants of the Bolzano-Weierstraß principle. We show that Ramsey's theorem for pairs implies a variant of the Bolzano-Weierstraß principle and, hence, show that our program extraction method is applicable to proofs using this principle. Also, we develop a method to extract programs from proofs that use non-principal ultrafilters and along with this we obtain a conservation result for the statement that a non-principal ultrafilter exists. This method is based on the techniques we developed for Ramsey's theorem for pairs.

Alternative Abstract:
Alternative AbstractLanguage
In dieser Arbeit untersuchen wir die beweistheoretische Stärke des Satzes von Ramsey für Paare. Wir entwickeln eine Methode, um Programme aus Beweisen, die diesen Satz verwenden, zu extrahieren. Des weiteren analysieren wir die Stärke von Varianten des Bolzano-Weierstraß Prinzips. Wir zeigen, dass der Satz von Ramsey eine Variante impliziert und dass damit unsere Programmextraktionsmethode anwendbar ist. Wir entwickeln auch eine Methode zur Extraktion von Programm aus Beweisen, die freie Ultrafilter verwenden. Die Methode basiert auf Techniken, die wir für die Extraktion von Programmen aus Beweisen, die den Satz von Ramsey verwenden, entwickelt haben.German
Uncontrolled Keywords: proof-mining, proof-theory, Ramsey's theorem for pairs, ultrafilters, Bolzano-Weierstrass, weak compactness, cohesive principle, chain antichain principle, functional interpretation, bar recursion
Classification DDC: 500 Naturwissenschaften und Mathematik > 510 Mathematik
Divisions: Fachbereich Mathematik
Fachbereich Mathematik > Logik
Date Deposited: 24 May 2012 09:37
Last Modified: 07 Dec 2012 12:04
Related URLs:
URN: urn:nbn:de:tuda-tuprints-29720
License: Simple publication rights for ULB
Referees: Kohlenbach, Prof. Dr. Ulrich and Avigad, Prof. PhD Jeremy and Martin, Prof. Dr. Ziegler
Refereed: 13 April 2012
URI: http://tuprints.ulb.tu-darmstadt.de/id/eprint/2972
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