Well-Ordering Principles and Pi 1,1-Comprehension + Bar Induction
Ian Alexander Thomson · White Rose eTheses Online (University of Leeds, The University of Sheffield, University of York) · 2017
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.