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Well-Ordering Principles and Pi 1,1-Comprehension + Bar Induction

Thomson, Ian Alexander (2017) Well-Ordering Principles and Pi 1,1-Comprehension + Bar Induction. PhD thesis, University of Leeds.

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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.

Item Type: Thesis (PhD)
Keywords: Proof Theory, Ordinal Analysis, Logic, Veblen Hierarchy, Cut Elimination, omega models
Academic Units: The University of Leeds > Faculty of Maths and Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds)
Depositing User: Mr Ian A Thomson
Date Deposited: 04 Dec 2018 16:57
Last Modified: 04 Dec 2018 16:57
URI: http://etheses.whiterose.ac.uk/id/eprint/22206

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