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Title: Complexities of proof-theoretical reductions
Author: Toppel, Michael
ISNI:       0000 0004 6062 2901
Awarding Body: University of Leeds
Current Institution: University of Leeds
Date of Award: 2016
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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.
Supervisor: Rathjen, Michael Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available