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Complexities of Proof-Theoretical Reductions

Toppel, Michael (2016) Complexities of Proof-Theoretical Reductions. PhD thesis, University of Leeds.

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Abstract

The present thesis is a contribution to a project that is carried out by Michael Rathjen and Andreas Weiermann to give a general method to study the proof-complexity of Pi_2 sentences. This general method uses the generalised ordinal-analysis that was given by Buchholz, Rueede and Strahm as well as the generalised characterisation of provable-recursive functions of PA with axioms for transfinite induction that was given by Weiermann. The present thesis links these two methods by giving an explicit elementary bound, for the proof-complexity increment that occurs after the transition from the theory that was used by Rueede and Strahm, to PA with axioms for transfinite induction, which was analysed by Weiermann.

Item Type: Thesis (PhD)
Keywords: proof theory, ordinal analysis, proof complexity, proof theoretical semantics
Academic Units: The University of Leeds > Faculty of Maths and Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds)
Identification Number/EthosID: uk.bl.ethos.705992
Depositing User: Michael Toppel
Date Deposited: 21 Mar 2017 10:02
Last Modified: 25 Jul 2018 09:54
URI: http://etheses.whiterose.ac.uk/id/eprint/16456

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