Thomson, Ian Alexander (2017) Well-Ordering Principles and Pi 1,1-Comprehension + Bar Induction. PhD thesis, University of Leeds.
Abstract
This thesis proves that the statement “Every set X is contained in a countable-coded omega-model of Pi �1,1-CA + Bar Induction” is equivalent to the statement, “For all sets X; if X is well-ordered, then the construction OT(E_(Omega_omega + X)) is well-ordered.” Here OT(E_(Omega_omega + X)) stands for the Veblen hierarchy up to
Omega_omega relativized through the addition of epsilon numbers E_X
above Omega_omega.
Metadata
Supervisors: | Rathjen, Michael |
---|---|
Keywords: | Proof Theory, Ordinal Analysis, Logic, Veblen Hierarchy, Cut Elimination, omega models |
Awarding institution: | University of Leeds |
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.759774 |
Depositing User: | Mr Ian A Thomson |
Date Deposited: | 04 Dec 2018 16:57 |
Last Modified: | 18 Feb 2020 12:32 |
Open Archives Initiative ID (OAI ID): | oai:etheses.whiterose.ac.uk:22206 |
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